Data commit

2023-07-01 11:58:00 -04:00 · 2023-07-01 11:58:00 -04:00 · cb5bb5e222
commit cb5bb5e222
parent 7387c8f97b
199093 changed files with 3378972 additions and 0 deletions
--- a/Task/Pascals-triangle-Puzzle/00-META.yaml
+++ b/Task/Pascals-triangle-Puzzle/00-META.yaml
@ -0,0 +1,2 @@
+---
+from: http://rosettacode.org/wiki/Pascal's_triangle/Puzzle
--- a/Task/Pascals-triangle-Puzzle/00-TASK.txt
+++ b/Task/Pascals-triangle-Puzzle/00-TASK.txt
@ -0,0 +1,17 @@
+This puzzle involves a [http://xunor.free.fr/en/riddles/auto/pyramidnb.php Pascals Triangle], also known as a [http://xunor.free.fr/en/riddles/auto/pyramidnb.php Pyramid of Numbers].
+<pre>
+           [ 151]
+          [  ][  ]
+        [40][  ][  ]
+      [  ][  ][  ][  ]
+    [ X][11][ Y][ 4][ Z]
+</pre>
+Each brick of the pyramid is the sum of the two bricks situated below it.<br>
+Of the three missing numbers at the base of the pyramid, 
+the middle one is the sum of the other two (that is, Y = X + Z).
+
+
+;Task:
+Write a program to find a solution to this puzzle.
+<br><br>
+
--- a/Task/Pascals-triangle-Puzzle/11l/pascals-triangle-puzzle.11l
+++ b/Task/Pascals-triangle-Puzzle/11l/pascals-triangle-puzzle.11l
@ -0,0 +1,43 @@
+F e(&x, row, col) -> &
+   R x[row * (row + 1) I/ 2 + col]
+
+F iterate(&v, &diff, do_print = 1B)
+   V tot = 0.0
+   L
+      e(&v, 0, 0) = 151
+      e(&v, 2, 0) = 40
+      e(&v, 4, 1) = 11
+      e(&v, 4, 3) = 4
+
+      L(i) 1..4
+         L(j) 0..i
+            e(&diff, i, j) = 0
+            I j < i
+               e(&diff, i, j) += e(&v, i - 1, j) - e(&v, i, j + 1) - e(&v, i, j)
+            I j != 0
+               e(&diff, i, j) += e(&v, i - 1, j - 1) - e(&v, i, j - 1) - e(&v, i, j)
+
+      L(i) 1..3
+         L(j) 0.<i
+            e(&diff, i, j) += e(&v, i + 1, j) + e(&v, i + 1, j + 1) - e(&v, i, j)
+
+      e(&diff, 4, 2) += e(&v, 4, 0) + e(&v, 4, 4) - e(&v, 4, 2)
+
+      L(i) 0 .< v.len
+         v[i] += diff[i] / 4
+
+      tot = sum(diff.map(a -> a * a))
+      I do_print
+         print(‘dev: ’tot)
+      I tot < 0.1
+         L.break
+
+V v = [0.0] * 15
+V diff = [0.0] * 15
+iterate(&v, &diff)
+
+V idx = 0
+L(i) 5
+   L(j) 0..i
+      print(‘#4’.format(Int(0.5 + v[idx])), end' I j < i {‘ ’} E "\n")
+      idx++
--- a/Task/Pascals-triangle-Puzzle/ALGOL-68/pascals-triangle-puzzle.alg
+++ b/Task/Pascals-triangle-Puzzle/ALGOL-68/pascals-triangle-puzzle.alg
@ -0,0 +1,96 @@
+MODE
+  FIELD = REAL,
+  VEC = [0]REAL,
+  MAT = [0,0]REAL;
+MODE BRICK = UNION(INT, CHAR);
+
+FLEX[][]BRICK puzzle = (
+           ( 151),
+         ( " ", " "),
+       (  40, " ", " "),
+     ( " ", " ", " ", " "),
+   ( "x",  11, "y",  4, "z")
+);
+
+PROC mat col = (INT row, col)INT: row*(row-1)OVER 2 + col;
+INT col x = mat col(5,1),
+    col y = mat col(5,3),
+    col z = mat col(5,5);
+
+OP INIT = (REF VEC vec)VOID: FOR elem FROM LWB vec TO UPB vec DO vec[elem]:=0 OD;
+OP INIT = (REF MAT mat)VOID: FOR row FROM LWB mat TO UPB mat DO INIT mat[row,] OD;
+
+OP / = (MAT a, MAT b)MAT:( # matrix division #
+  [LWB b:UPB b]INT p ;
+  INT sign;
+  [,]FIELD lu = lu decomp(b, p, sign);
+  [LWB a:UPB a, 1 LWB a:2 UPB a]FIELD out;
+  FOR col FROM 2 LWB a TO 2 UPB a DO out[,col] := lu solve(b, lu, p, a[,col]) OD;
+  out
+);
+
+OP / = (VEC a, MAT b)VEC: ( # vector division #
+  [LWB a:UPB a,1]FIELD transpose a;
+  transpose a[,1]:=a;
+  (transpose a/b)[,LWB a]
+);
+
+INT upb mat = mat col(UPB puzzle, UPB puzzle);
+[upb mat, upb mat] REAL mat; INIT mat;
+[upb mat] REAL vec; INIT vec;
+
+INT mat row := LWB mat;
+INT known row := UPB mat - UPB puzzle + 1;
+
+# build the simultaneous equation to solve #
+FOR row FROM LWB puzzle TO UPB puzzle DO
+  FOR col FROM LWB puzzle[row] TO UPB puzzle[row] DO
+    IF row < UPB puzzle THEN
+      mat[mat row, mat col(row, col)] := 1;
+      mat[mat row, mat col(row+1, col)] := -1;
+      mat[mat row, mat col(row+1, col+1)] := -1;
+      mat row +:= 1
+    FI;
+    CASE puzzle[row][col] IN
+      (INT value):(
+        mat[known row, mat col(row, col)] := 1;
+        vec[known row] := value;
+        known row +:= 1
+      ),
+      (CHAR variable):SKIP
+    ESAC
+  OD
+OD;
+
+# finally add x - y + z = 0 #
+mat[known row, col x] := 1;
+mat[known row, col y] := -1;
+mat[known row, col z] := 1;
+
+FORMAT real repr = $g(-5,2)$;
+
+CO # print details of the simultaneous equation being solved #
+FORMAT
+  vec repr = $"("n(2 UPB mat-1)(f(real repr)", ")f(real repr)")"$,
+  mat repr = $"("n(1 UPB mat-1)(f(vec repr)", "lx)f(vec repr)")"$;
+
+printf(($"Vec: "l$,vec repr, vec, $l$));
+printf(($"Mat: "l$,mat repr, mat, $l$));
+END CO
+
+# finally actually solve the equation #
+VEC solution vec = vec/mat;
+
+# and wrap up by printing the solution #
+FLEX[UPB puzzle]FLEX[0]REAL solution;
+FOR row FROM LWB puzzle TO UPB puzzle DO
+  solution[row] := LOC[row]REAL;
+  FOR col FROM LWB puzzle[row] TO UPB puzzle[row] DO
+    solution[row][col] := solution vec[mat col(row, col)]
+  OD;
+  printf(($n(UPB puzzle-row)(4x)$, $x"("f(real repr)")"$, solution[row], $l$))
+OD;
+
+FOR var FROM 1 BY 2 TO 5 DO
+  printf(($5x$,$g$,puzzle[UPB puzzle][var],"=", real repr, solution[UPB puzzle][var]))
+OD
--- a/Task/Pascals-triangle-Puzzle/Ada/pascals-triangle-puzzle.ada
+++ b/Task/Pascals-triangle-Puzzle/Ada/pascals-triangle-puzzle.ada
@ -0,0 +1,69 @@
+with Ada.Text_IO; use Ada.Text_IO;
+
+procedure Pyramid_of_Numbers is
+
+   B_X, B_Y, B_Z : Integer := 0; -- Unknown variables
+
+   type Block_Value is record
+      Known   : Integer := 0;
+      X, Y, Z : Integer := 0;
+   end record;
+   X : constant Block_Value := (0, 1, 0, 0);
+   Y : constant Block_Value := (0, 0, 1, 0);
+   Z : constant Block_Value := (0, 0, 0, 1);
+   procedure Add (L : in out Block_Value; R : Block_Value) is
+   begin -- Symbolically adds one block to another
+      L.Known := L.Known + R.Known;
+      L.X := L.X + R.X - R.Z; -- Z is excluded as n(Y - X - Z) = 0
+      L.Y := L.Y + R.Y + R.Z;
+   end Add;
+   procedure Add (L : in out Block_Value; R : Integer) is
+   begin -- Symbolically adds a value to the block
+      L.Known := L.Known + R;
+   end Add;
+
+   function Image (N : Block_Value) return String is
+   begin -- The block value, when X,Y,Z are known
+      return Integer'Image (N.Known + N.X * B_X + N.Y * B_Y + N.Z * B_Z);
+   end Image;
+
+   procedure Solve_2x2 (A11, A12, B1, A21, A22, B2 : Integer) is
+   begin -- Don't care about things, supposing an integer solution exists
+      if A22 = 0 then
+         B_X := B2 / A21;
+         B_Y := (B1 - A11*B_X) / A12;
+      else
+         B_X := (B1*A22 - B2*A12) / (A11*A22 - A21*A12);
+         B_Y := (B1 - A11*B_X) / A12;
+      end if;
+      B_Z := B_Y - B_X;
+   end Solve_2x2;
+
+   B : array (1..5, 1..5) of Block_Value; -- The lower triangle contains blocks
+
+begin
+   -- The bottom blocks
+   Add (B(5,1),X); Add (B(5,2),11); Add (B(5,3),Y); Add (B(5,4),4); Add (B(5,5),Z);
+
+   -- Upward run
+   for Row in reverse 1..4 loop
+      for Column in 1..Row loop
+         Add (B (Row, Column), B (Row + 1, Column));
+         Add (B (Row, Column), B (Row + 1, Column + 1));
+      end loop;
+   end loop;
+
+   -- Now have known blocks 40=(3,1), 151=(1,1) and Y=X+Z to determine X,Y,Z
+   Solve_2x2
+   (  B(1,1).X, B(1,1).Y, 151 - B(1,1).Known,
+      B(3,1).X, B(3,1).Y,  40 - B(3,1).Known
+   );
+
+   -- Print the results
+   for Row in 1..5 loop
+      New_Line;
+      for Column in 1..Row loop
+         Put (Image (B(Row,Column)));
+      end loop;
+   end loop;
+end Pyramid_of_Numbers;
--- a/Task/Pascals-triangle-Puzzle/AutoHotkey/pascals-triangle-puzzle-1.ahk
+++ b/Task/Pascals-triangle-Puzzle/AutoHotkey/pascals-triangle-puzzle-1.ahk
@ -0,0 +1,4 @@
+N1 := 11, N2 := 4, N3 := 40, N4 := 151
+Z := (2*N4 - 7*N3 - 8*N2 + 6*N1) / 7
+X := (N3 - 2*N1 - Z) / 2
+MsgBox,, Pascal's Triangle, %X%`n%Z%
--- a/Task/Pascals-triangle-Puzzle/AutoHotkey/pascals-triangle-puzzle-2.ahk
+++ b/Task/Pascals-triangle-Puzzle/AutoHotkey/pascals-triangle-puzzle-2.ahk
@ -0,0 +1,274 @@
+;---------------------------------------------------------------------------
+; Pascal's triangle.ahk
+; by wolf_II
+;---------------------------------------------------------------------------
+; http://rosettacode.org/wiki/Pascal's_triangle/Puzzle
+;---------------------------------------------------------------------------
+
+
+
+;---------------------------------------------------------------------------
+AutoExecute: ; auto-execute section of the script
+;---------------------------------------------------------------------------
+    #SingleInstance, Force          ; only one instance allowed
+    #NoEnv                          ; don't check empty variables
+    ;-----------------------------------------------------------------------
+    AppName := "Pascal's triangle"
+    N1 := 11, N2 := 4, N3 := 40, N4 := 151
+
+    ; monitor MouseMove events
+    OnMessage(0x0200, "WM_MOUSEMOVE")
+
+    ; GUI
+    Gosub, GuiCreate
+    Gui, Show,, %AppName%
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+GuiCreate: ; create the GUI
+;---------------------------------------------------------------------------
+    Gui, -MinimizeBox
+    Gui, Margin, 8, 8
+
+    ; 15 edit controls
+    Loop, 5
+        Loop, % Row := A_Index {
+            xx := 208 + (A_Index - 5) * 50 - (Row - 5) * 25
+            yy := 8 + (Row - 1) * 22
+            vv := Row "_" A_Index
+            Gui, Add, Edit, x%xx% y%yy% w50 v%vv% Center ReadOnly -TabStop
+        }
+    GuiControl, -WantReturn, Edit11
+    GuiControl, -WantReturn, Edit15
+
+    ; buttons (2 hidden)
+    Gui, Add, Button, x8 w78, &Restart
+    Gui, Add, Button, x+8 wp, &Solve
+    Gui, Add, Button, x+8 wp, &Check
+    Gui, Add, Button, x8 wp, Cle&ar
+    Gui, Add, Button, xp wp Hidden, &Cancel
+    Gui, Add, Button, x+8 wp, &New
+    Gui, Add, Button, xp wp Hidden, &Apply
+    Gui, Add, Button, x+8 wp, E&xit
+
+    ; status bar
+    Gui, Add, StatusBar
+
+    ; blue font
+    Gui, Font, bold cBlue
+    GuiControl, Font, Edit11
+    GuiControl, Font, Edit15
+    ; falling through
+
+;---------------------------------------------------------------------------
+ButtonRestart: ; restart retaining the blue clues
+;---------------------------------------------------------------------------
+    Controls(True) ; enable controls
+    Loop, 15
+        If A_Index Not In 1,4,11,12,14,15
+            GuiControl,, Edit%A_Index% ; clear
+    GuiControl,, Edit1, %N4%
+    GuiControl,, Edit4, %N3%
+    GuiControl,, Edit12, %N1%
+    GuiControl,, Edit14, %N2%
+    GuiControl,, Edit11, %X%
+    GuiControl,, Edit15, %Z%
+    GreenFont:
+    Gui, Font, bold cGreen
+    GuiControl, Font, Edit1
+    GuiControl, Font, Edit4
+    GuiControl, Font, Edit12
+    GuiControl, Font, Edit14
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+ButtonSolve: ; calculate solution
+;---------------------------------------------------------------------------
+    ; N1 := 11    N2 := 4    N3 := 40    N4 := 151
+    ;-----------------------------------------------------------------------
+    ; Y = X + Z
+    ; 40  = (11+X) + (11+Y)
+    ; A   = (11+Y) + (Y+4)
+    ; B   =  (4+Y) + (4+Z)
+    ; 151 = (40+A) + (A+B)
+    ;-----------------------------------------------------------------------
+    Gosub, GreenFont
+    GuiControl,, Edit15, % Z := Round( (2*N4 - 7*N3 - 8*N2 + 6*N1) / 7 )
+    GuiControl,, Edit11, % X := Round( (N3 - 2*N1 - Z) / 2 )
+    ; falling through
+
+;---------------------------------------------------------------------------
+ButtonCheck: ; check the [entry|solution] for errors
+;---------------------------------------------------------------------------
+    Controls(False) ; disable controls
+    Gui, Submit, NoHide
+    X := 5_1, Z := 5_5
+    Loop, 5
+        Loop, % Row := A_Index
+            If (%Row%_%A_Index% = "")
+                %Row%_%A_Index% := 0
+    GuiControl,, Edit13, % 5_3 := 5_1 + 5_5
+    GuiControl,, Edit10, % 4_4 := 5_4 + 5_5
+    GuiControl,, Edit9,  % 4_3 := 5_3 + 5_4
+    GuiControl,, Edit8,  % 4_2 := 5_2 + 5_3
+    GuiControl,, Edit7,  % 4_1 := 5_1 + 5_2
+    GuiControl,, Edit6,  % 3_3 := 4_4 + 4_3
+    GuiControl,, Edit5,  % 3_2 := 4_3 + 4_2
+    GuiControl,, Edit4,  % 3_1 := 4_2 + 4_1
+    GuiControl,, Edit3,  % 2_2 := 3_3 + 3_2
+    GuiControl,, Edit2,  % 2_1 := 3_2 + 3_1
+    GuiControl,, Edit1,  % 1_1 := 2_2 + 2_1
+    Gui, Font, bold cRed
+    If Not 3_1 = N3
+        GuiControl, Font, Edit4
+    If Not 1_1 = N4
+        GuiControl, Font, Edit1
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+ButtonClear: ; restart without the blue clues
+;---------------------------------------------------------------------------
+    X := Z := ""
+    Gosub, ButtonRestart
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+ButtonNew: ; enter new numbers for the puzzle
+;---------------------------------------------------------------------------
+    Gosub, GreenFont
+    Loop, 15
+        If A_Index Not In 1,4,12,14
+            GuiControl,, Edit%A_Index% ; clear
+    Controls(False) ; disable controls
+    NewContr(True)  ; enable controls for new numbers
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+ButtonApply: ; remember the new numbers
+;---------------------------------------------------------------------------
+    Gui, Submit, NoHide
+    N1 := 5_2, N2 := 5_4, N3 := 3_1, N4 := 1_1
+    NewContr(False) ; disable controls for new numbers
+    Controls(True)  ; enable controls
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+ButtonCancel: ; restore the old numbers
+;---------------------------------------------------------------------------
+    GuiControl,, Edit1, %N4%
+    GuiControl,, Edit4, %N3%
+    GuiControl,, Edit12, %N1%
+    GuiControl,, Edit14, %N2%
+    NewContr(False) ; disable controls for new numbers
+    Controls(True)  ; enable controls
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+GuiClose:
+;---------------------------------------------------------------------------
+GuiEscape:
+;---------------------------------------------------------------------------
+ButtonExit:
+;---------------------------------------------------------------------------
+    ; common action
+    ExitApp
+
+Return
+
+
+
+;---------------------------------------------------------------------------
+Controls(Bool) { ; [dis|re-en]able some controls
+;---------------------------------------------------------------------------
+    Enable  := Bool ? "+" : "-"
+    Disable := Bool ? "-" : "+"
+
+    GuiControl, %Disable%ReadOnly, Edit11
+    GuiControl, %Disable%ReadOnly, Edit15
+    GuiControl, %Enable%TabStop, Edit11
+    GuiControl, %Enable%TabStop, Edit15
+
+    GuiControl, %Disable%Default, &Restart
+    GuiControl, %Enable%Default, &Check
+    GuiControl, %Disable%Disabled, &Check
+    GuiControl, %Enable%Disabled, &Restart
+}
+
+
+
+;---------------------------------------------------------------------------
+NewContr(Bool) { ; [dis|re-en]able control for new numbers
+;---------------------------------------------------------------------------
+    Enable  := Bool ? "+" : "-"
+    Disable := Bool ? "-" : "+"
+
+    GuiControl, %Disable%ReadOnly, Edit1
+    GuiControl, %Disable%ReadOnly, Edit4
+    GuiControl, %Disable%ReadOnly, Edit12
+    GuiControl, %Disable%ReadOnly, Edit14
+
+    GuiControl, %Enable%TabStop, Edit1
+    GuiControl, %Enable%TabStop, Edit4
+    GuiControl, %Enable%TabStop, Edit12
+    GuiControl, %Enable%TabStop, Edit14
+
+    GuiControl, %Enable%Hidden, Button1
+    GuiControl, %Enable%Hidden, Button2
+    GuiControl, %Enable%Hidden, Button3
+    GuiControl, %Enable%Hidden, Button4
+    GuiControl, %Disable%Hidden, Button5
+    GuiControl, %Enable%Hidden, Button6
+    GuiControl, %Disable%Hidden, Button7
+    GuiControl, %Enable%Hidden, Button8
+
+}
+
+
+
+;---------------------------------------------------------------------------
+WM_MOUSEMOVE() { ; monitor MouseMove events
+;---------------------------------------------------------------------------
+    ; display quick help in StatusBar
+    ;-----------------------------------------------------------------------
+    global AppName
+    CurrControl := A_GuiControl
+    IfEqual True,, MsgBox ; dummy
+
+    ; mouse is over buttons
+    Else If (CurrControl = "&Restart")
+        SB_SetText("restart retaining the blue clues")
+    Else If (CurrControl = "&Solve")
+        SB_SetText("calculate solution")
+    Else If (CurrControl = "&Check")
+        SB_SetText("check if the entries are correct")
+    Else If (CurrControl = "Cle&ar")
+        SB_SetText("restart without the blue clues")
+    Else If (CurrControl = "&New")
+        SB_SetText("enter new numbers for the puzzle")
+    Else If (CurrControl = "E&xit")
+        SB_SetText("exit " AppName)
+
+    ; delete status bar text
+    Else SB_SetText("")
+}
--- a/Task/Pascals-triangle-Puzzle/BBC-BASIC/pascals-triangle-puzzle.basic
+++ b/Task/Pascals-triangle-Puzzle/BBC-BASIC/pascals-triangle-puzzle.basic
@ -0,0 +1,39 @@
+      INSTALL @lib$ + "ARRAYLIB"
+
+      REM Describe the puzzle as a set of simultaneous equations:
+      REM  a + b = 151
+      REM  a - c = 40
+      REM  -b + c + d = 0
+      REM  e + f = 40
+      REM  -c + f + g = 0
+      REM  -d + g + h = 0
+      REM  e - x = 11
+      REM  f - y = 11
+      REM  g - y = 4
+      REM  h - z = 4
+      REM  x - y + z = 0
+      REM So we have 11 equations in 11 unknowns.
+
+      REM We can represent these equations as a matrix and a vector:
+      DIM matrix(10,10), vector(10)
+      matrix() = \ a, b, c, d, e, f, g, h, x, y, z
+      \            1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, \
+      \            1, 0,-1, 0, 0, 0, 0, 0, 0, 0, 0, \
+      \            0,-1, 1, 1, 0, 0, 0, 0, 0, 0, 0, \
+      \            0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, \
+      \            0, 0,-1, 0, 0, 1, 1, 0, 0, 0, 0, \
+      \            0, 0, 0,-1, 0, 0, 1, 1, 0, 0, 0, \
+      \            0, 0, 0, 0, 1, 0, 0, 0,-1, 0, 0, \
+      \            0, 0, 0, 0, 0, 1, 0, 0, 0,-1, 0, \
+      \            0, 0, 0, 0, 0, 0, 1, 0, 0,-1, 0, \
+      \            0, 0, 0, 0, 0, 0, 0, 1, 0, 0,-1, \
+      \            0, 0, 0, 0, 0, 0, 0, 0, 1,-1, 1
+      vector() = 151, 40, 0, 40, 0, 0, 11, 11, 4, 4, 0
+
+      REM Now solve the simultaneous equations:
+      PROC_invert(matrix())
+      vector() = matrix().vector()
+
+      PRINT "X = " ; vector(8)
+      PRINT "Y = " ; vector(9)
+      PRINT "Z = " ; vector(10)
--- a/Task/Pascals-triangle-Puzzle/C++/pascals-triangle-puzzle.cpp
+++ b/Task/Pascals-triangle-Puzzle/C++/pascals-triangle-puzzle.cpp
@ -0,0 +1,65 @@
+#include <iostream>
+#include <iomanip>
+
+inline int sign(int i) {
+    return i < 0 ? -1 : i > 0;
+}
+
+inline int& E(int *x, int row, int col) {
+    return x[row * (row + 1) / 2 + col];
+}
+
+int iter(int *v, int *diff) {
+    // enforce boundary conditions
+    E(v, 0, 0) = 151;
+    E(v, 2, 0) = 40;
+    E(v, 4, 1) = 11;
+    E(v, 4, 3) = 4;
+
+    // calculate difference from equilibrium
+    for (auto i = 1u; i < 5u; i++)
+        for (auto j = 0u; j <= i; j++) {
+            E(diff, i, j) = 0;
+            if (j < i)
+                E(diff, i, j) += E(v, i - 1, j) - E(v, i, j + 1) - E(v, i, j);
+            if (j)
+                E(diff, i, j) += E(v, i - 1, j - 1) - E(v, i, j - 1) - E(v, i, j);
+        }
+
+    for (auto i = 0u; i < 4u; i++)
+        for (auto j = 0u; j < i; j++)
+            E(diff, i, j) += E(v, i + 1, j) + E(v, i + 1, j + 1) - E(v, i, j);
+
+    E(diff, 4, 2) += E(v, 4, 0) + E(v, 4, 4) - E(v, 4, 2);
+
+    // do feedback, check if we are done
+    uint sum;
+    int e = 0;
+    for (auto i = sum = 0u; i < 15u; i++) {
+        sum += !!sign(e = diff[i]);
+
+        // 1/5-ish feedback strength on average.  These numbers are highly magical, depending on nodes' connectivities
+        if (e >= 4 || e <= -4)
+            v[i] += e / 5;
+        else if (rand() < RAND_MAX / 4)
+            v[i] += sign(e);
+    }
+    return sum;
+}
+
+void show(int *x) {
+    for (auto i = 0u; i < 5u; i++)
+        for (auto j = 0u; j <= i; j++)
+            std::cout << std::setw(4u) << *(x++) << (j < i ? ' ' : '\n');
+}
+
+int main() {
+    int v[15] = { 0 }, diff[15] = { 0 };
+    for (auto i = 1u, s = 1u; s; i++) {
+        s = iter(v, diff);
+        std::cout << "pass " << i << ": " << s << std::endl;
+    }
+    show(v);
+
+    return 0;
+}
--- a/Task/Pascals-triangle-Puzzle/C-sharp/pascals-triangle-puzzle.cs
+++ b/Task/Pascals-triangle-Puzzle/C-sharp/pascals-triangle-puzzle.cs
@ -0,0 +1,186 @@
+using System;
+
+namespace Pyramid_of_Numbers
+{
+        class Program
+	{
+		public static void Main(string[] args)
+		{
+			// Set console properties
+			Console.Title = " Pyramid of Numbers  /  Pascal's triangle Puzzle";
+			Console.SetBufferSize(80,1000);
+			Console.SetWindowSize(80,60);
+			Console.ForegroundColor = ConsoleColor.Green;
+
+			
+			// Main Program Loop
+			ConsoleKeyInfo k = new ConsoleKeyInfo('Y', ConsoleKey.Y,true,true,true);
+			while (k.Key == ConsoleKey.Y)
+			{
+				Console.Clear();
+				
+				Console.WriteLine("----------------------------------------------");
+				Console.WriteLine(" Pyramid of Numbers / Pascal's triangle Puzzle");
+				Console.WriteLine("----------------------------------------------");
+				Console.WriteLine();
+
+				
+				
+				//
+				// Declare new Pyramid array
+				//
+				int r = 5;// Number of rows
+				int [,] Pyramid = new int[r,r];
+				
+				// Set initial Pyramid values
+				for (int i = 0; i < r; i++)
+				{
+					for(int j = 0; j < r; j++)
+					{
+						Pyramid[i,j] = 0;
+					}
+				}
+				// Show info on created array
+				Console.WriteLine(" Pyramid has " + r + " rows");
+				Console.WriteLine("--------------------------------------------");
+				
+				// Enter Pyramid values
+				for(int i = 0; i <= r-1; i++)
+				{
+					Console.WriteLine(" Enter " + (i+1).ToString() + ". row values:");
+					Console.WriteLine("--------------------------------------------");
+					
+					for(int j = 0; j < i+1; j++)
+					{
+						Console.Write(" " + (j+1).ToString() + ". value = ");
+						int v = int.Parse(Console.ReadLine());
+						
+						Pyramid[i,j] = v;
+					}
+					Console.WriteLine("--------------------------------------------");
+				}
+				
+				//
+				// Show initial Pyramid values
+				//
+				Console.WriteLine();
+				Console.WriteLine(" Initial Pyramid Values ");
+				Console.WriteLine();
+				
+				// Show Pyramid values
+				for(int i = 0; i <= r-1; i++)
+				{
+					for(int j = 0; j < i+1; j++)
+					{
+						Console.Write("{0,4}",Pyramid[i,j]);
+					}
+					Console.WriteLine();
+				}
+				Console.WriteLine("--------------------------------------------");
+				
+				// Find solution
+				Solve_Pyramid(Pyramid);
+				
+				Console.WriteLine();
+				Console.Write(" Start new calculation <Y/N>  . . . ");
+				k = Console.ReadKey(true);
+			}
+		}
+		
+                //
+                // Solve Function
+                //
+		public static void Solve_Pyramid(int [,] Pyramid)
+		{
+			int r = 5; // Number of rows
+			
+			// Calculate Y
+			int a = Pyramid[r-1,1];
+			int b = Pyramid[r-1,3];
+			int c = Pyramid[0,0];
+			
+			int y =  (c - (4*a) - (4*b))/7;
+			Pyramid[r-1,2] = y;
+			
+			
+			// Create copy of Pyramid
+			int [,] Pyramid_Copy = new int[r,r];
+			Array.Copy(Pyramid,Pyramid_Copy,r*r);
+			
+			int n = 0; // solution counter
+			for(int x = 0; x < y + 1; x++)
+			{
+				for(int z = 0; z < y + 1; z++)
+				{
+					if( (x+z) == y)
+					{
+						Pyramid[r-1,0]   = x;
+						Pyramid[r-1,r-1] = z;
+						
+						// Recalculate Pyramid values
+						for(int i = r-1; i > 0; i--)
+						{
+							for(int j = 0; j < i; j++)
+							{
+								Pyramid[i-1,j] = Pyramid[i,j]+Pyramid[i,j+1];
+							}
+						}
+						
+						
+						// Compare Pyramid values
+						bool solved = true;
+						for(int i = 0; i < r-1; i++)
+						{
+							for(int j = 0; j < i+1; j++)
+							{
+								if(Pyramid_Copy[i,j]>0)
+								{
+									if(Pyramid[i,j] != Pyramid_Copy[i,j])
+									{
+										solved = false;
+										i = r;
+										break;
+									}
+								}
+							}
+						}
+						
+						if(solved)
+						{
+							n++;
+							Console.WriteLine();
+							Console.WriteLine(" Solved Pyramid Values no." + n);
+							Console.WriteLine();
+							
+							// Show Pyramid values
+							for(int i = 0; i <= r-1; i++)
+							{
+								for(int j = 0; j < i+1; j++)
+								{
+									Console.Write("{0,4}",Pyramid[i,j]);
+								}
+								Console.WriteLine();
+							}
+							Console.WriteLine();
+							Console.WriteLine(" X = " + Pyramid[r-1,0] + "   " +
+							                  " Y = " + Pyramid[r-1,2] + "   " +
+							                  " Z = " + Pyramid[r-1,4]);
+							Console.WriteLine();
+							Console.WriteLine("--------------------------------------------");
+						}
+						
+						Array.Copy(Pyramid_Copy,Pyramid,r*r);
+					}
+				}
+			}
+			
+			if(n == 0)
+			{
+				Console.WriteLine();
+				Console.WriteLine(" Pyramid has no solution ");
+				Console.WriteLine();
+			}
+		}
+		
+	}
+}
--- a/Task/Pascals-triangle-Puzzle/C/pascals-triangle-puzzle-1.c
+++ b/Task/Pascals-triangle-Puzzle/C/pascals-triangle-puzzle-1.c
@ -0,0 +1,39 @@
+/* Pascal's pyramid solver
+ *
+ *               [top]
+ *            [   ] [   ]
+ *         [mid] [   ] [   ]
+ *      [   ] [   ] [   ] [   ]
+ *   [ x ] [ a ] [ y ] [ b ] [ z ]
+ *             x + z = y
+ *
+ * This solution makes use of a little bit of mathematical observation,
+ * such as the fact that top = 4(a+b) + 7(x+z) and mid = 2x + 2a + z.
+ */
+
+#include <stdio.h>
+#include <math.h>
+
+void pascal(int a, int b, int mid, int top, int* x, int* y, int* z)
+{
+    double ytemp = (top - 4 * (a + b)) / 7.;
+    if(fmod(ytemp, 1.) >= 0.0001)
+    {
+        x = 0;
+        return;
+    }
+    *y = ytemp;
+    *x = mid - 2 * a - *y;
+    *z = *y - *x;
+}
+int main()
+{
+    int a = 11, b = 4, mid = 40, top = 151;
+    int x, y, z;
+    pascal(a, b, mid, top, &x, &y, &z);
+    if(x != 0)
+        printf("x: %d, y: %d, z: %d\n", x, y, z);
+    else printf("No solution\n");
+
+    return 0;
+}
--- a/Task/Pascals-triangle-Puzzle/C/pascals-triangle-puzzle-2.c
+++ b/Task/Pascals-triangle-Puzzle/C/pascals-triangle-puzzle-2.c
@ -0,0 +1,73 @@
+#include <stdio.h>
+#include <stdlib.h>
+
+void show(int *x) {
+	int i, j;
+
+	for (i = 0; i < 5; i++)
+		for (j = 0; j <= i; j++)
+			printf("%4d%c", *(x++), j < i ? ' ' : '\n');
+}
+
+inline int sign(int i)
+{
+	return i < 0 ? -1 : i > 0;
+}
+
+int iter(int *v, int *diff) {
+	int sum, i, j, e = 0;
+
+#	define E(x, row, col) x[(row) * ((row) + 1) / 2 + (col)]
+	/* enforce boundary conditions */
+	E(v, 0, 0) = 151;
+	E(v, 2, 0) = 40;
+	E(v, 4, 1) = 11;
+	E(v, 4, 3) = 4;
+
+	/* calculate difference from equilibrium */
+	for (i = 1; i < 5; i++) {
+		for (j = 0; j <= i; j++) {
+			E(diff, i, j) = 0;
+			if (j < i)
+				E(diff, i, j) += E(v, i - 1, j) -
+						 E(v, i, j + 1) -
+						 E(v, i, j);
+			if (j)
+				E(diff, i, j) += E(v, i - 1, j - 1) -
+						 E(v, i, j - 1) -
+						 E(v, i, j);
+		}
+	}
+
+	for (i = 0; i < 4; i++)
+		for (j = 0; j < i; j++)
+			E(diff, i, j) += E(v, i + 1, j) +
+					 E(v, i + 1, j + 1) -
+					 E(v, i, j);
+
+	E(diff, 4, 2) += E(v, 4, 0) + E(v, 4, 4) - E(v, 4, 2);
+#	undef E
+
+	/* Do feedback, check if we are done. */
+	for (i = sum = 0; i < 15; i++) {
+		sum += !!sign(e = diff[i]);
+
+		/* 1/5-ish feedback strength on average.  These numbers are highly
+		   magical, depending on nodes' connectivities. */
+		if (e >= 4 || e <= -4) 		v[i] += e/5;
+		else if (rand() < RAND_MAX/4)	v[i] += sign(e);
+	}
+	return sum;
+}
+
+int main() {
+	int v[15] = { 0 }, diff[15] = { 0 }, i, s;
+
+	for (i = s = 1; s; i++) {
+		s = iter(v, diff);
+		printf("pass %d: %d\n", i, s);
+	}
+	show(v);
+
+	return 0;
+}
--- a/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-1.clj
+++ b/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-1.clj
@ -0,0 +1,9 @@
+(def bottom [ [0 1 0], [11 0 0], [0 1 1], [4 0 0], [0 0 1] ])
+
+(defn plus  [v1 v2] (vec (map + v1 v2)))
+(defn minus [v1 v2] (vec (map - v1 v2)))
+(defn scale [n v]   (vec (map #(* n %) v )))
+
+(defn above [row] (map #(apply plus %) (partition 2 1 row)))
+
+(def rows (reverse (take 5 (iterate above bottom))))
--- a/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-2.clj
+++ b/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-2.clj
@ -0,0 +1,5 @@
+(def c00 (get-in rows [0 0]))
+(def c20 (get-in rows [2 0]))
+
+(def eqn0 (minus c00 [151 0 0]))
+(def eqn1 (minus c20 [ 40 0 0]))
--- a/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-3.clj
+++ b/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-3.clj
@ -0,0 +1,11 @@
+(defn solve [m]
+  (assert (<= 1 m 2))
+  (let [n  (- 3 m)
+        v0 (scale (eqn1 n) eqn0)
+        v1 (scale (eqn0 n) eqn1)
+        vd (minus v0 v1)]
+    (assert (zero? (vd n)))
+    (/ (- (vd 0)) (vd m))))
+
+(let [x (solve 1), z (solve 2), y (+ x z)]
+  (println "x =" x ", y =" y ", z =" z))
--- a/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-4.clj
+++ b/Task/Pascals-triangle-Puzzle/Clojure/pascals-triangle-puzzle-4.clj
@ -0,0 +1,5 @@
+(defn dot [v1 v2] (reduce + (map * v1 v2)))
+
+(defn show-pyramid [x z]
+  (doseq [row rows]
+    (println (map #(dot [1 x z] %) row)))
--- a/Task/Pascals-triangle-Puzzle/Craft-Basic/pascals-triangle-puzzle.basic
+++ b/Task/Pascals-triangle-Puzzle/Craft-Basic/pascals-triangle-puzzle.basic
@ -0,0 +1,53 @@
+let x = -1
+
+do
+
+	let x = x + 1
+	let z = 0
+
+	do
+
+		let e = x + 11
+		let f = 11 + (x + z)
+		let g = (x + z) + 4
+		let h = 4 + z
+
+		if e + f = 40 then
+
+			let c = f + g
+			let d = g + h
+			let a = 40 + c
+			let b = c + d
+			let q = 0
+
+			if a + b = 151 then
+
+				let q = 1
+
+			endif
+
+		endif
+
+		if q = 0 then
+
+			let z = z + 1
+
+		endif
+
+		wait
+
+	loopwhile z < 20 and q = 0
+
+	if q = 0 then
+
+		let z = -1
+
+	endif
+
+	wait
+
+loopuntil z >= 0
+
+print "x = ", x
+print "y = ", x + z
+print "z = ", z
--- a/Task/Pascals-triangle-Puzzle/Curry/pascals-triangle-puzzle.curry
+++ b/Task/Pascals-triangle-Puzzle/Curry/pascals-triangle-puzzle.curry
@ -0,0 +1,25 @@
+import CLPFD
+import Constraint (allC, andC)
+import Findall (findall)
+import List (init, last)
+
+
+solve :: [[Int]] -> Success
+solve body@([n]:rest) =
+    domain (concat body) 1 n
+  & andC (zipWith atop body rest)
+  & labeling [] (concat body)
+  where
+    xs `atop` ys = andC $ zipWith3 tri xs (init ys) (tail ys)
+
+tri :: Int -> Int -> Int -> Success
+tri x y z = x =# y +# z
+
+test (x,y,z) | tri y x z =
+    [ [151]
+    , [ _,  _]
+    , [40,  _, _]
+    , [ _,  _, _, _]
+    , [ x, 11, y, 4, z]
+    ]
+main = findall $ solve . test
--- a/Task/Pascals-triangle-Puzzle/D/pascals-triangle-puzzle.d
+++ b/Task/Pascals-triangle-Puzzle/D/pascals-triangle-puzzle.d
@ -0,0 +1,61 @@
+import std.stdio, std.algorithm;
+
+void iterate(bool doPrint=true)(double[] v, double[] diff) @safe {
+    static ref T E(T)(T[] x, in size_t row, in size_t col)
+    pure nothrow @safe @nogc {
+        return x[row * (row + 1) / 2 + col];
+    }
+
+    double tot = 0.0;
+    do {
+        // Enforce boundary conditions.
+        E(v, 0, 0) = 151;
+        E(v, 2, 0) = 40;
+        E(v, 4, 1) = 11;
+        E(v, 4, 3) = 4;
+
+        // Calculate difference from equilibrium.
+        foreach (immutable i; 1 .. 5) {
+            foreach (immutable j; 0 .. i + 1) {
+                E(diff, i, j) = 0;
+                if (j < i)
+                    E(diff, i, j) += E(v, i - 1, j) - E(v, i, j + 1) - E(v, i, j);
+                if (j)
+                    E(diff, i, j) += E(v, i - 1, j - 1) - E(v, i, j - 1) - E(v, i, j);
+            }
+        }
+
+        foreach (immutable i; 1 .. 4)
+            foreach (immutable j; 0 .. i)
+                E(diff, i, j) += E(v, i + 1, j) + E(v, i + 1, j + 1) - E(v, i, j);
+
+        E(diff, 4, 2) += E(v, 4, 0) + E(v, 4, 4) - E(v, 4, 2);
+
+        // Do feedback, check if we are close enough.
+        // 4: scale down the feedback to avoid oscillations.
+        v[] += diff[] / 4;
+        tot = diff.map!q{ a ^^ 2 }.sum;
+
+        static if (doPrint)
+            writeln("dev: ", tot);
+
+        // tot(dx^2) < 0.1 means each cell is no more than 0.5 away
+        // from equilibrium. It takes about 50 iterations. After
+        // 700 iterations tot is < 1e-25, but that's overkill.
+    } while (tot >= 0.1);
+}
+
+void main() {
+    static void show(in double[] x) nothrow @nogc {
+        int idx;
+        foreach (immutable i; 0 .. 5)
+            foreach (immutable j; 0 .. i+1) {
+                printf("%4d%c", cast(int)(0.5 + x[idx]), j < i ? ' ' : '\n');
+                idx++;
+            }
+    }
+
+    double[15] v = 0.0, diff = 0.0;
+    iterate(v, diff);
+    show(v);
+}
--- a/Task/Pascals-triangle-Puzzle/F-Sharp/pascals-triangle-puzzle.fs
+++ b/Task/Pascals-triangle-Puzzle/F-Sharp/pascals-triangle-puzzle.fs
@ -0,0 +1,23 @@
+#load"Packages\MathNet.Numerics.FSharp\MathNet.Numerics.fsx"
+
+open MathNet.Numerics.LinearAlgebra
+
+let A = matrix [
+                    [ 1.; 1.; 0.; 0.; 0.; 0.; 0.; 0.; 0.; 0.; 0. ]
+                    [ -1.;  0.; 1.; 0.; 0.; 0.; 0.; 0.; 0.; 0.; 0. ]
+                    [ 0.; -1.; 1.; 1.; 0.; 0.; 0.; 0.; 0.; 0.; 0. ]
+                    [ 0.; 0.; 0.; 0.; 1.; 1.; 0.; 0.; 0.; 0.; 0. ]
+                    [ 0.; 0.; -1.; 0.; 0.; 1.; 1.; 0.; 0.; 0.; 0. ]
+                    [ 0.; 0.; 0.; -1.; 0.; 0.; 1.; 1.; 0.; 0.; 0. ]
+                    [ 0.; 0.; 0.; 0.; -1.; 0.; 0.; 0.; 1.; 0.; 0. ]
+                    [ 0.; 0.; 0.; 0.; 0.; -1.; 0.; 0.; 0.; 1.; 0. ]
+                    [ 0.; 0.; 0.; 0.; 0.; 0.; -1.; 0.; 0.; 1.; 0. ]
+                    [ 0.; 0.; 0.; 0.; 0.; 0.; 0.; -1.; 0.; 0.; 1. ]
+                    [ 0.; 0.; 0.; 0.; 0.; 0.; 0.; 0.; 1.; -1.; 1. ]
+                ]
+
+let b = vector [151.; -40.; 0.; 40.; 0.; 0.; -11.; -11.; -4.; -4.; 0.]
+
+let x = A.Solve(b)
+
+printfn "x = %f, Y = %f, Z = %f" x.[8] x.[9] x.[10]
--- a/Task/Pascals-triangle-Puzzle/Factor/pascals-triangle-puzzle.factor
+++ b/Task/Pascals-triangle-Puzzle/Factor/pascals-triangle-puzzle.factor
@ -0,0 +1,13 @@
+USING: arrays backtrack combinators.extras fry grouping.extras
+interpolate io kernel math math.ranges sequences ;
+
+: base ( ?x ?z -- seq ) 2dup + swap '[ _ 11 _ 4 _ ] >array ;
+
+: up ( seq -- seq' ) [ [ + ] 2clump-map ] twice ;
+
+: find-solution ( -- x z )
+    10 [1,b] dup [ amb-lazy ] bi@ 2dup base
+    up dup first 40 = must-be-true
+    up first 151 = must-be-true ;
+
+find-solution [I X = ${1}, Z = ${}I] nl
--- a/Task/Pascals-triangle-Puzzle/FreeBASIC/pascals-triangle-puzzle.basic
+++ b/Task/Pascals-triangle-Puzzle/FreeBASIC/pascals-triangle-puzzle.basic
@ -0,0 +1,28 @@
+Function SolveForZ(x As Integer) As Integer
+    Dim As Integer a, b, c, d, e, f, g, h, z
+    For z = 0 To 20
+        e = x + 11
+        f = 11 + (x+z)
+        g = (x+z) + 4
+        h = 4 + z
+        If e + f = 40 Then
+            c = f + g
+            d = g + h
+            a = 40 + c
+            b = c + d
+            If a + b = 151 Then Return z
+        End If
+    Next z
+    Return -1
+End Function
+
+Dim As Integer x = -1, z = 0
+Do
+    x = x + 1
+    z = SolveForZ(x)
+Loop Until z >= 0
+
+Print "X ="; x
+Print "Y ="; x + z
+Print "Z ="; z
+Sleep
--- a/Task/Pascals-triangle-Puzzle/Go/pascals-triangle-puzzle.go
+++ b/Task/Pascals-triangle-Puzzle/Go/pascals-triangle-puzzle.go
@ -0,0 +1,134 @@
+package main
+
+import "fmt"
+
+// representation of an expression in x, y, and z
+type expr struct {
+    x, y, z float64 // coefficients
+    c       float64 // constant term
+}
+
+// add two expressions
+func addExpr(a, b expr) expr {
+    return expr{a.x + b.x, a.y + b.y, a.z + b.z, a.c + b.c}
+}
+
+// subtract two expressions
+func subExpr(a, b expr) expr {
+    return expr{a.x - b.x, a.y - b.y, a.z - b.z, a.c - b.c}
+}
+
+// multiply expression by a constant
+func mulExpr(a expr, c float64) expr {
+    return expr{a.x * c, a.y * c, a.z * c, a.c * c}
+}
+
+// given a row of expressions, produce the next row up, by the given
+// sum relation between blocks
+func addRow(l []expr) []expr {
+    if len(l) == 0 {
+        panic("wrong")
+    }
+    r := make([]expr, len(l)-1)
+    for i := range r {
+        r[i] = addExpr(l[i], l[i+1])
+    }
+    return r
+}
+
+// given expression b in a variable, and expression a,
+// take b == 0 and substitute to remove that variable from a.
+func substX(a, b expr) expr {
+    if b.x == 0 {
+        panic("wrong")
+    }
+    return subExpr(a, mulExpr(b, a.x/b.x))
+}
+
+func substY(a, b expr) expr {
+    if b.y == 0 {
+        panic("wrong")
+    }
+    return subExpr(a, mulExpr(b, a.y/b.y))
+}
+
+func substZ(a, b expr) expr {
+    if b.z == 0 {
+        panic("wrong")
+    }
+    return subExpr(a, mulExpr(b, a.z/b.z))
+}
+
+// given an expression in a single variable, return value of that variable
+func solveX(a expr) float64 {
+    if a.x == 0 || a.y != 0 || a.z != 0 {
+        panic("wrong")
+    }
+    return -a.c / a.x
+}
+
+func solveY(a expr) float64 {
+    if a.x != 0 || a.y == 0 || a.z != 0 {
+        panic("wrong")
+    }
+    return -a.c / a.y
+}
+
+func solveZ(a expr) float64 {
+    if a.x != 0 || a.y != 0 || a.z == 0 {
+        panic("wrong")
+    }
+    return -a.c / a.z
+}
+
+func main() {
+    // representation of given information for bottom row
+    r5 := []expr{{x: 1}, {c: 11}, {y: 1}, {c: 4}, {z: 1}}
+    fmt.Println("bottom row:", r5)
+
+    // given definition of brick sum relation
+    r4 := addRow(r5)
+    fmt.Println("next row up:", r4)
+    r3 := addRow(r4)
+    fmt.Println("middle row:", r3)
+
+    // given relation y = x + z
+    xyz := subExpr(expr{y: 1}, expr{x: 1, z: 1})
+    fmt.Println("xyz relation:", xyz)
+    // remove z from third cell using xyz relation
+    r3[2] = substZ(r3[2], xyz)
+    fmt.Println("middle row after substituting for z:", r3)
+
+    // given cell = 40,
+    b := expr{c: 40}
+    // this gives an xy relation
+    xy := subExpr(r3[0], b)
+    fmt.Println("xy relation:", xy)
+    // substitute 40 for cell
+    r3[0] = b
+
+    // remove x from third cell using xy relation
+    r3[2] = substX(r3[2], xy)
+    fmt.Println("middle row after substituting for x:", r3)
+
+    // continue applying brick sum relation to get top cell
+    r2 := addRow(r3)
+    fmt.Println("next row up:", r2)
+    r1 := addRow(r2)
+    fmt.Println("top row:", r1)
+
+    // given top cell = 151, we have an equation in y
+    y := subExpr(r1[0], expr{c: 151})
+    fmt.Println("y relation:", y)
+    // using xy relation, we get an equation in x
+    x := substY(xy, y)
+    fmt.Println("x relation:", x)
+    // using xyz relation, we get an equation in z
+    z := substX(substY(xyz, y), x)
+    fmt.Println("z relation:", z)
+
+    // show final answers
+    fmt.Println("x =", solveX(x))
+    fmt.Println("y =", solveY(y))
+    fmt.Println("z =", solveZ(z))
+}
--- a/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-1.hs
+++ b/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-1.hs
@ -0,0 +1 @@
+puzzle = [["151"],["",""],["40","",""],["","","",""],["X","11","Y","4","Z"]]
--- a/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-2.hs
+++ b/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-2.hs
@ -0,0 +1,29 @@
+triangle n = n * (n+1) `div` 2
+
+coeff xys x = maybe 0 id $ lookup x xys
+
+row n cs = [coeff cs k | k <- [1..n]]
+
+eqXYZ n = [(0, 1:(-1):1:replicate n 0)]
+
+eqPyramid n h = do
+  a <- [1..h-1]
+  x <- [triangle (a-1) + 1 .. triangle a]
+  let y = x+a
+  return $ (0, 0:0:0:row n [(x,-1),(y,1),(y+1,1)])
+
+eqConst n fields = do
+  (k,s) <- zip [1..] fields
+  guard $ not $ null s
+  return $ case s of
+    "X" - (0, 1:0:0:row n [(k,-1)])
+    "Y" - (0, 0:1:0:row n [(k,-1)])
+    "Z" - (0, 0:0:1:row n [(k,-1)])
+    _   - (fromInteger $ read s, 0:0:0:row n [(k,1)])
+
+equations :: [[String]] - ([Rational], [[Rational]])
+equations puzzle = unzip eqs where
+  fields = concat puzzle
+  eqs = eqXYZ n ++ eqPyramid n h ++ eqConst n fields
+  h = length puzzle
+  n = length fields
--- a/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-3.hs
+++ b/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-3.hs
@ -0,0 +1,10 @@
+normalize :: [Rational] - [Integer]
+normalize xs = [numerator (x * v) | x <- xs] where
+  v = fromInteger $ foldr1 lcm $ map denominator $ xs
+
+run puzzle = map (normalize . drop 3) $ answer where
+  (a, m) = equations puzzle
+  lr = decompose 0 m
+  answer = case solve 0 lr a of
+    Nothing - []
+    Just x  - x : kernel lr
--- a/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-4.hs
+++ b/Task/Pascals-triangle-Puzzle/Haskell/pascals-triangle-puzzle-4.hs
@ -0,0 +1,4 @@
+*Main run puzzle
+[[151,81,70,40,41,29,16,24,17,12,5,11,13,4,8]]
+*Main run [[""],["2",""],["X","Y","Z"]]
+[[3,2,1,1,1,0],[3,0,3,-1,1,2]]
--- a/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-1.j
+++ b/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-1.j
@ -0,0 +1 @@
+chk=:40 151&-:@(2 4{{."1)
--- a/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-2.j
+++ b/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-2.j
@ -0,0 +1 @@
+base=: [,11,+,4,]
--- a/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-3.j
+++ b/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-3.j
@ -0,0 +1 @@
+ord=:5
--- a/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-4.j
+++ b/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-4.j
@ -0,0 +1 @@
+    |."2(#~chk"2) 2(+/\)^:(<ord)"1 base/"1>,{ ;~i:28
--- a/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-5.j
+++ b/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-5.j
@ -0,0 +1 @@
+,.(1+i.5)<@{."0 1{.|."2(#~chk"2) 2(+/\)^:(<ord)"1 base/"1>,{ ;~i:28
--- a/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-6.j
+++ b/Task/Pascals-triangle-Puzzle/J/pascals-triangle-puzzle-6.j
@ -0,0 +1 @@
+,.(<@{."0 1~1+i.@#){.|."2(#~chk"2) 2(+/\)^:(<ord)"1 base/"1>,{ ;~i:28
--- a/Task/Pascals-triangle-Puzzle/Java/pascals-triangle-puzzle.java
+++ b/Task/Pascals-triangle-Puzzle/Java/pascals-triangle-puzzle.java
@ -0,0 +1,113 @@
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+public class PascalsTrianglePuzzle {
+
+    public static void main(String[] args) {
+        Matrix mat = new Matrix(Arrays.asList(1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 0d, 0d),
+                                Arrays.asList(0d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 0d),
+                                Arrays.asList(0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 1d, -1d),
+                                Arrays.asList(0d, 0d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, -1d, 0d),
+                                Arrays.asList(0d, 0d, 0d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, -1d),
+                                Arrays.asList(1d, 1d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d, 0d),
+                                Arrays.asList(0d, 1d, 1d, 0d, -1d, 0d, 0d, 0d, 0d, 0d, 0d),
+                                Arrays.asList(0d, 0d, 1d, 1d, 0d, -1d, 0d, 0d, 0d, 0d, 0d),
+                                Arrays.asList(0d, 0d, 0d, 0d, -1d, 0d, 1d, 0d, 0d, 0d, 0d),
+                                Arrays.asList(0d, 0d, 0d, 0d, 1d, 1d, 0d, -1d, 0d, 0d, 0d),
+                                Arrays.asList(0d, 0d, 0d, 0d, 0d, 0d, 1d, 1d, 0d, 0d, 0d));
+        List<Double> b = Arrays.asList(11d, 11d, 0d, 4d, 4d, 40d, 0d, 0d, 40d, 0d, 151d);
+        List<Double> solution = cramersRule(mat, b);
+        System.out.println("Solution = " + cramersRule(mat, b));
+        System.out.printf("X = %.2f%n", solution.get(8));
+        System.out.printf("Y = %.2f%n", solution.get(9));
+        System.out.printf("Z = %.2f%n", solution.get(10));
+    }
+
+    private static List<Double> cramersRule(Matrix matrix, List<Double> b) {
+        double denominator = matrix.determinant();
+        List<Double> result = new ArrayList<>();
+        for ( int i = 0 ; i < b.size() ; i++ ) {
+            result.add(matrix.replaceColumn(b, i).determinant() / denominator);
+        }
+        return result;
+    }
+
+    private static class Matrix {
+
+        private List<List<Double>> matrix;
+
+        @Override
+        public String toString() {
+            return matrix.toString();
+        }
+
+        @SafeVarargs
+        public Matrix(List<Double> ... lists) {
+            matrix = new ArrayList<>();
+            for ( List<Double> list : lists) {
+                matrix.add(list);
+            }
+        }
+
+        public Matrix(List<List<Double>> mat) {
+            matrix = mat;
+        }
+
+        public double determinant() {
+            if ( matrix.size() == 1 ) {
+                return get(0, 0);
+            }
+            if ( matrix.size() == 2 ) {
+                return get(0, 0) * get(1, 1) - get(0, 1) * get(1, 0);
+            }
+            double sum = 0;
+            double sign = 1;
+            for ( int i = 0 ; i < matrix.size() ; i++ ) {
+                sum += sign * get(0, i) * coFactor(0, i).determinant();
+                sign *= -1;
+            }
+            return sum;
+        }
+
+        private Matrix coFactor(int row, int col) {
+            List<List<Double>> mat = new ArrayList<>();
+            for ( int i = 0 ; i < matrix.size() ; i++ ) {
+                if ( i == row ) {
+                    continue;
+                }
+                List<Double> list = new ArrayList<>();
+                for ( int j = 0 ; j < matrix.size() ; j++ ) {
+                    if ( j == col ) {
+                        continue;
+                    }
+                    list.add(get(i, j));
+                }
+                mat.add(list);
+            }
+            return new Matrix(mat);
+        }
+
+        private Matrix replaceColumn(List<Double> b, int column) {
+            List<List<Double>> mat = new ArrayList<>();
+            for ( int row = 0 ; row < matrix.size() ; row++ ) {
+                List<Double> list = new ArrayList<>();
+                for ( int col = 0 ; col < matrix.size() ; col++ ) {
+                    double value = get(row, col);
+                    if ( col == column ) {
+                        value = b.get(row);
+                    }
+                    list.add(value);
+                }
+                mat.add(list);
+            }
+            return new Matrix(mat);
+        }
+
+        private double get(int row, int col) {
+            return matrix.get(row).get(col);
+        }
+
+    }
+
+}
--- a/Task/Pascals-triangle-Puzzle/Jq/pascals-triangle-puzzle-1.jq
+++ b/Task/Pascals-triangle-Puzzle/Jq/pascals-triangle-puzzle-1.jq
@ -0,0 +1,17 @@
+def solve(r11; r31; r52; r54):
+  range(1;r31 - 1) as $X
+  | range(1; r31 - 1) as $Y
+  | (($Y - $X) | select(. > 0)) as $Z
+  | (r52 + $X) as $R41
+  | (r52 + $Y) as $R42
+  | select($R41 + $R42 == r31)
+  | ($Y + r54) as $R43
+  | (r54 + $Z) as $R44
+  | ($R42 + $R43) as $R32
+  | ($R43 + $R44) as $R33
+  | (r31 + $R32) as $R21
+  | ($R32 + $R33) as $R22
+  | select($R21 + $R22 == r11)
+  | [$X, $Y, $Z];
+
+solve(151; 40; 11; 4),
--- a/Task/Pascals-triangle-Puzzle/Jq/pascals-triangle-puzzle-2.jq
+++ b/Task/Pascals-triangle-Puzzle/Jq/pascals-triangle-puzzle-2.jq
@ -0,0 +1,8 @@
+include "rc-cramers-rule";
+def solve(top; mid; a; b):
+  cramer(
+     [ [7, 7],
+       [2,  1]];
+     [top - 4*(a+b), mid-2*a]);
+
+solve(151; 40; 11; 4)
--- a/Task/Pascals-triangle-Puzzle/Julia/pascals-triangle-puzzle.julia
+++ b/Task/Pascals-triangle-Puzzle/Julia/pascals-triangle-puzzle.julia
@ -0,0 +1,14 @@
+function pascal(a::Integer, b::Integer, mid::Integer, top::Integer)
+    yd = round((top - 4 * (a + b)) / 7)
+    !isinteger(yd) && return 0, 0, 0
+    y  = Int(yd)
+    x  = mid - 2a - y
+    return x, y, y - x
+end
+
+x, y, z = pascal(11, 4, 40, 151)
+if !iszero(x)
+    println("Solution: x = $x, y = $y, z = $z.")
+else
+    println("There is no solution.")
+end
--- a/Task/Pascals-triangle-Puzzle/Kotlin/pascals-triangle-puzzle.kotlin
+++ b/Task/Pascals-triangle-Puzzle/Kotlin/pascals-triangle-puzzle.kotlin
@ -0,0 +1,22 @@
+// version 1.1.3
+
+data class Solution(val x: Int, val y: Int, val z: Int)
+
+fun Double.isIntegral(tolerance: Double = 0.0) =
+    (this - Math.floor(this)) <= tolerance || (Math.ceil(this) - this) <= tolerance
+
+fun pascal(a: Int, b: Int, mid: Int, top: Int): Solution {
+    val yd = (top - 4 * (a + b)) / 7.0
+    if (!yd.isIntegral(0.0001)) return Solution(0, 0, 0)
+    val y = yd.toInt()
+    val x = mid - 2 * a - y
+    return Solution(x, y, y - x)
+}
+
+fun main(args: Array<String>) {
+    val (x, y, z) = pascal(11, 4, 40, 151)
+    if (x != 0)
+        println("Solution is: x = $x, y = $y, z = $z")
+    else
+        println("There is no solutuon")
+}
--- a/Task/Pascals-triangle-Puzzle/Maple/pascals-triangle-puzzle.maple
+++ b/Task/Pascals-triangle-Puzzle/Maple/pascals-triangle-puzzle.maple
@ -0,0 +1,2 @@
+sys := {22 + x + y = 40, 78 + 5*y + z = 151, x + z = y}:
+solve(sys, {x,y,z});
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-1.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-1.math
@ -0,0 +1,11 @@
+b+c==a
+d+e==b
+e+f==c
+g+h==d
+h+i==e
+i+j==f
+l+X==g
+l+Y==h
+n+Y==i
+n+Z==j
+X+Z==Y
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-2.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-2.math
@ -0,0 +1,4 @@
+a->151
+d->40
+l->11
+n->4
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-3.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-3.math
@ -0,0 +1,3 @@
+eqs={a==b+c,d+e==b,e+f==c,g+h==d,h+i==e,i+j==f,l+X==g,l+Y==h,n+Y==i,n+Z==j,Y==X+Z};
+knowns={a->151,d->40,l->11,n->4};
+Solve[eqs/.knowns,{b,c,e,f,g,h,i,j,X,Y,Z}]
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-4.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-4.math
@ -0,0 +1 @@
+{{b -> 81, c -> 70, e -> 41, f -> 29, g -> 16, h -> 24, i -> 17,  j -> 12, X -> 5, Y -> 13, Z -> 8}}
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-5.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-5.math
@ -0,0 +1,5 @@
+				151
+			81		70
+		40		41		29
+	16		24		17		12
+5		11		13		4		8
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-6.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-6.math
@ -0,0 +1,2 @@
+triangle[n_, m_] :=  Nest[MovingMap[Total, #, 1] &, {x, 11, y, 4, z}, n - 1][[m]]
+Solve[{triangle[3, 1] == 40, triangle[5, 1] == 151, y == x + z}, {x, y, z}]
--- a/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-7.math
+++ b/Task/Pascals-triangle-Puzzle/Mathematica/pascals-triangle-puzzle-7.math
@ -0,0 +1 @@
+{{x -> 5, y -> 13, z -> 8}}
--- a/Task/Pascals-triangle-Puzzle/MiniZinc/pascals-triangle-puzzle.minizinc
+++ b/Task/Pascals-triangle-Puzzle/MiniZinc/pascals-triangle-puzzle.minizinc
@ -0,0 +1,14 @@
+%Pascal's Triangle Puzzle. Nigel Galloway, February 17th., 2020
+int: N11=151; constraint N11=N21+N22;
+var 1..N11: N21=N31+N32;
+var 1..N11: N22=N32+N33;
+int: N31=40; constraint N31=N41+N42;
+var 1..N11: N32=N42+N43;
+var 1..N11: N33=N43+N44;
+var 1..N11: N41=X+11;
+var 1..N11: N42=Y+11;
+var 1..N11: N43=Y+4;
+var 1..N11: N44=Z+4;
+var 1..N11: X;
+var 1..N11: Y=X+Z;
+var 1..N11: Z;
--- a/Task/Pascals-triangle-Puzzle/Nim/pascals-triangle-puzzle.nim
+++ b/Task/Pascals-triangle-Puzzle/Nim/pascals-triangle-puzzle.nim
@ -0,0 +1,60 @@
+import strutils
+
+type
+
+  BlockValue = object
+    known: int
+    x, y, z: int
+
+  Variables = tuple[x, y, z: int]
+
+func `+=`(left: var BlockValue; right: BlockValue) =
+  ## Symbolically add one block to another.
+  left.known += right.known
+  left.x += right.x - right.z    # Z is excluded as n(Y - X - Z) = 0.
+  left.y += right.y + right.z
+
+proc toString(n: BlockValue; vars: Variables): string =
+  ## Return the representation of the block value, when X, Y, Z are known.
+  result = $(n.known + n.x * vars.x + n.y * vars.y + n.z * vars.z)
+
+proc Solve2x2(a11, a12, b1, a21, a22, b2: int): Variables =
+  ## Solve a puzzle, supposing an integer solution exists.
+  if a22 == 0:
+    result.x = b2 div a21
+    result.y = (b1 - a11 * result.x) div a12
+  else:
+    result.x = (b1 * a22 - b2 * a12) div (a11 * a22 - a21 * a12)
+    result.y = (b1 - a11 * result.x) div a12
+  result.z = result.y - result.x
+
+var blocks : array[1..5, array[1..5, BlockValue]]   # The lower triangle contains blocks.
+
+# The bottom blocks.
+blocks[5][1] = BlockValue(x: 1)
+blocks[5][2] = BlockValue(known: 11)
+blocks[5][3] = BlockValue(y: 1)
+blocks[5][4] = BlockValue(known: 4)
+blocks[5][5] = BlockValue(z: 1)
+
+# Upward run.
+for row in countdown(4, 1):
+  for column in 1..row:
+    blocks[row][column] += blocks[row + 1][column]
+    blocks[row][column] += blocks[row + 1][column + 1]
+
+# Now have known blocks 40=[3][1], 151=[1][1] and Y=X+Z to determine X,Y,Z.
+let vars = Solve2x2(blocks[1][1].x,
+                    blocks[1][1].y,
+                    151 - blocks[1][1].known,
+                    blocks[3][1].x,
+                    blocks[3][1].y,
+                    40 - blocks[3][1].known)
+
+# Print the results.
+for row in 1..5:
+  var line = ""
+  for column in 1..row:
+    line.addSep(" ")
+    line.add toString(blocks[row][column], vars)
+  echo line
--- a/Task/Pascals-triangle-Puzzle/Oz/pascals-triangle-puzzle.oz
+++ b/Task/Pascals-triangle-Puzzle/Oz/pascals-triangle-puzzle.oz
@ -0,0 +1,69 @@
+%% to compile : ozc -x <file.oz>
+functor
+
+import
+  System Application FD Search
+define
+
+  proc{Quest Root Rules}
+
+    proc{Limit Rc Ls}
+      case Ls of nil then skip
+      [] X|Xs then
+        {Limit Rc Xs}
+        case X of N#V then
+          Rc.N =: V
+        [] N1#N2#N3 then
+          Rc.N1 =: Rc.N2 + Rc.N3
+        end
+      end
+    end
+
+    proc {Pyramid R}
+      {FD.tuple solution 15 0#FD.sup R}  %% non-negative integers domain
+  %%          01      , pyramid format
+  %%        02  03
+  %%      04  05  06
+  %%    07  08  09  10
+  %%  11  12  13  14  15
+      R.1 =: R.2 + R.3     %% constraints of Pyramid of numbers
+      R.2 =: R.4 + R.5
+      R.3 =: R.5 + R.6
+      R.4 =: R.7 + R.8
+      R.5 =: R.8 + R.9
+      R.6 =: R.9 + R.10
+      R.7 =: R.11 + R.12
+      R.8 =: R.12 + R.13
+      R.9 =: R.13 + R.14
+      R.10 =: R.14 + R.15
+
+      {Limit R Rules}      %% additional constraints
+
+      {FD.distribute ff R}
+    end
+  in
+    {Search.base.one Pyramid Root} %% search for solution
+  end
+
+  local
+    Root R
+  in
+    {Quest Root [1#151 4#40 12#11 14#4 13#11#15]} %% supply additional constraint rules
+    if {Length Root} >= 1 then
+      R = Root.1
+      {For 1 15 1
+        proc{$ I}
+          if {Member I [1 3 6 10]} then
+            {System.printInfo R.I#'\n'}
+          else
+            {System.printInfo R.I#' '}
+          end
+        end
+      }
+    else
+      {System.showInfo 'No solution found.'}
+    end
+  end
+
+  {Application.exit 0}
+end
--- a/Task/Pascals-triangle-Puzzle/PARI-GP/pascals-triangle-puzzle.parigp
+++ b/Task/Pascals-triangle-Puzzle/PARI-GP/pascals-triangle-puzzle.parigp
@ -0,0 +1,5 @@
+Pascals_triangle_puzzle(topvalue=151,leftsidevalue=40,bottomvalue1=11,bottomvalue2=4) = {
+y=(topvalue-(4*(bottomvalue1+bottomvalue2)))/7;
+x=leftsidevalue-(y+2*bottomvalue1);
+z=y-x;
+print(x","y","z); }
--- a/Task/Pascals-triangle-Puzzle/Perl/pascals-triangle-puzzle.pl
+++ b/Task/Pascals-triangle-Puzzle/Perl/pascals-triangle-puzzle.pl
@ -0,0 +1,40 @@
+# set up triangle
+my $rows = 5;
+my @tri = map { [ map { {x=>0,z=>0,v=>0,rhs=>undef} } 1..$_ ] } 1..$rows;
+$tri[0][0]{rhs} = 151;
+$tri[2][0]{rhs} = 40;
+$tri[4][0]{x} = 1;
+$tri[4][1]{v} = 11;
+$tri[4][2]{x} = 1;
+$tri[4][2]{z} = 1;
+$tri[4][3]{v} = 4;
+$tri[4][4]{z} = 1;
+
+# aggregate from bottom to top
+for my $row ( reverse 0..@tri-2 ) {
+    for my $col ( 0..@{$tri[$row]}-1 ){
+        $tri[$row][$col]{$_} = $tri[$row+1][$col]{$_}+$tri[$row+1][$col+1]{$_} for 'x','z','v';
+    }
+}
+# find equations
+my @eqn;
+for my $row ( @tri ) {
+    for my $col ( @$row ){
+        push @eqn, [ $$col{x}, $$col{z}, $$col{rhs}-$$col{v} ] if defined $$col{rhs};
+    }
+}
+# print equations
+print "Equations:\n";
+print "  x +   z = y\n";
+printf "%d x + %d z = %d\n", @$_ for @eqn;
+# solve
+my $f = $eqn[0][1] / $eqn[1][1];
+$eqn[0][$_] -=  $f * $eqn[1][$_] for 0..2;
+$f = $eqn[1][0] / $eqn[0][0];
+$eqn[1][$_] -=  $f * $eqn[0][$_] for 0..2;
+# print solution
+print "Solution:\n";
+my $x = $eqn[0][2]/$eqn[0][0];
+my $z = $eqn[1][2]/$eqn[1][1];
+my $y = $x+$z;
+printf "x=%d, y=%d, z=%d\n", $x, $y, $z;
--- a/Task/Pascals-triangle-Puzzle/Phix/pascals-triangle-puzzle-1.phix
+++ b/Task/Pascals-triangle-Puzzle/Phix/pascals-triangle-puzzle-1.phix
@ -0,0 +1,137 @@
+(phixonline)-->
+ <span style="color: #000080;font-style:italic;">--
+ -- demo\rosetta\Pascal_triangle_Puzzle.exw
+ -- =======================================
+ --
+ -- I approached this with a view to solving general pyramid puzzles, not just the one given.
+ --
+ -- This little ditty converts the pyramid to rules quite nicely, then uses a modified copy
+ --  of solveN() from [[Solving_coin_problems#Phix]] to solve those simultaneous equations.
+ --</span>
+ <span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
+
+ <span style="color: #004080;">sequence</span> <span style="color: #000000;">pyramid</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">151</span><span style="color: #0000FF;">},</span>
+                    <span style="color: #0000FF;">{</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">},</span>
+                   <span style="color: #0000FF;">{</span><span style="color: #000000;">40</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">},</span>
+                  <span style="color: #0000FF;">{</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">,</span><span style="color: #008000;">""</span><span style="color: #0000FF;">},</span>
+                <span style="color: #0000FF;">{</span><span style="color: #008000;">"x"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"y"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">4</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"z"</span><span style="color: #0000FF;">}}</span>
+
+ <span style="color: #004080;">sequence</span> <span style="color: #000000;">rules</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{}</span>
+
+ <span style="color: #000080;font-style:italic;">-- each cell in the pyramid is either an integer final value or an equation.
+ -- initially the equations are strings, we substitute all with triplets of
+ -- the form {k,x,z} ie k+l*x+m*z, and known values &lt; last row become rules.</span>
+
+ <span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">5</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
+         <span style="color: #004080;">object</span> <span style="color: #000000;">prc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">],</span> <span style="color: #000000;">equ</span>
+         <span style="color: #008080;">if</span>    <span style="color: #000000;">prc</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"x"</span> <span style="color: #008080;">then</span>  <span style="color: #000000;">prc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>     <span style="color: #000080;font-style:italic;">-- ie 0 + one x</span>
+         <span style="color: #008080;">elsif</span> <span style="color: #000000;">prc</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"y"</span> <span style="color: #008080;">then</span>  <span style="color: #000000;">prc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>     <span style="color: #000080;font-style:italic;">-- ie 0 + one x plus one z</span>
+         <span style="color: #008080;">elsif</span> <span style="color: #000000;">prc</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"z"</span> <span style="color: #008080;">then</span>  <span style="color: #000000;">prc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>     <span style="color: #000080;font-style:italic;">-- ie 0 +            one z</span>
+         <span style="color: #008080;">else</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">prc</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">or</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span>
+                 <span style="color: #000080;font-style:italic;">-- examples: x+11 is {0,1,0}+{11,0,0} -&gt; {11,1,0},
+                 --           11+y is {11,0,0}+{0,1,1} -&gt; {11,1,1},
+                 --       40=""+"" is {40,0,0}={22,2,1} ==&gt; {18,2,1}</span>
+                 <span style="color: #000000;">equ</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_add</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">],</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">prc</span><span style="color: #0000FF;">=</span><span style="color: #008000;">""</span> <span style="color: #008080;">then</span>  <span style="color: #000000;">prc</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">equ</span>
+             <span style="color: #008080;">else</span>            <span style="color: #000000;">prc</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">prc</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span>
+                             <span style="color: #008080;">if</span> <span style="color: #000000;">r</span><span style="color: #0000FF;"><=</span><span style="color: #000000;">4</span> <span style="color: #008080;">then</span>
+                                 <span style="color: #000000;">equ</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">prc</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]-</span><span style="color: #000000;">equ</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+                                 <span style="color: #000000;">rules</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">append</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">,</span><span style="color: #000000;">equ</span><span style="color: #0000FF;">)</span>
+                             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">prc</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+
+ <span style="color: #7060A8;">ppOpt</span><span style="color: #0000FF;">({</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_StrFmt</span><span style="color: #0000FF;">,</span><span style="color: #000000;">2</span><span style="color: #0000FF;">,</span><span style="color: #004600;">pp_IntCh</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">})</span>
+ <span style="color: #0000FF;">?</span><span style="color: #008000;">"equations"</span>
+ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">)</span>
+ <span style="color: #0000FF;">?</span><span style="color: #008000;">"rules"</span>
+ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">)</span>   <span style="color: #000080;font-style:italic;">-- {18,2,1} === 18=2x+z
+             -- {73,5,6} === 73=5x+6z</span>
+ <span style="color: #7060A8;">puts</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"=====\n"</span><span style="color: #0000FF;">)</span>
+
+ <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">)==</span><span style="color: #000000;">2</span><span style="color: #0000FF;">)</span>    <span style="color: #000080;font-style:italic;">-- more work needed!?
+
+ -- modified copy of solveN() from Solving_coin_problems.exw as promised, a
+ -- bit of a sledgehammer to crack a peanut is the phrase you are looking for:</span>
+ <span style="color: #008080;">function</span> <span style="color: #000000;">solveN</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">)</span>
+ <span style="color: #000080;font-style:italic;">--
+ -- Based on https://mathcs.clarku.edu/~djoyce/ma105/simultaneous.html
+ --  aka the ancient Chinese Jiuzhang suanshu ~100 B.C. (!!)
+ --
+ -- Example (not related to the task problem):
+ --  rules = <nowiki>{{</nowiki>18,1,1},{38,1,5<nowiki>}}</nowiki>, ie 18==x+y, 38==x+5y
+ --  ==&gt; {13,5}, ie x=13, y=5
+ --
+ --  In the elimination phase, both x have multipliers of 1, ie both rii and rij are 1,
+ --  so we can ignore the two sq_mul and just do [sq_sub] (38=x+5y)-(18=x+y)==&gt;(20=4y).
+ --  Obviously therefore y is 5 and substituting backwards x is 13.
+ --
+ -- Example2 (taken from the task problem):
+ --  rules = <nowiki>{{</nowiki>18,2,1},{73,5,6<nowiki>}}</nowiki>, ie 18==2x+z, 73==5x+6z
+ --      ==&gt; <nowiki>{{</nowiki>18,2,1},{56,0,7<nowiki>}}</nowiki>, ie rules[2]:=rules[2]*2-rules[1]*5     (eliminate)
+ --      ==&gt; <nowiki>{{</nowiki>18,2,1},8},        ie rules[2]:=56/7, aka z:=8            (substitute)
+ --      ==&gt; <nowiki>{{</nowiki>10,2,0},8},        ie rules[1]-=1z                        (substitute)
+ --      ==&gt; {5,8},               ie rules[1]:=10/2, aka x:=5            (substitute)
+ --  ==&gt; {5,8}, ie x=5, z=8
+ -- </span>
+     <span style="color: #004080;">sequence</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rj</span>
+     <span style="color: #004080;">integer</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">),</span> <span style="color: #000000;">rii</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rji</span>
+     <span style="color: #000000;">rules</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">)</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
+         <span style="color: #000080;font-style:italic;">-- successively eliminate (grow lower left triangle of 0s)</span>
+         <span style="color: #000000;">ri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
+         <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">)=</span><span style="color: #000000;">l</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">)</span>
+         <span style="color: #000000;">rii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+         <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rii</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span>  <span style="color: #000080;font-style:italic;">-- (see note below)</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">l</span> <span style="color: #008080;">do</span>
+             <span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
+             <span style="color: #000000;">rji</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
+                 <span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sq_sub</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rj</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rii</span><span style="color: #0000FF;">),</span><span style="color: #7060A8;">sq_mul</span><span style="color: #0000FF;">(</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rji</span><span style="color: #0000FF;">))</span>
+                 <span style="color: #7060A8;">assert</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">0</span><span style="color: #0000FF;">)</span> <span style="color: #000080;font-style:italic;">-- (job done)</span>
+                 <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">l</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
+         <span style="color: #000080;font-style:italic;">-- then substitute each backwards</span>
+         <span style="color: #000000;">ri</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span>
+         <span style="color: #000000;">rii</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]/</span><span style="color: #000000;">ri</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #000080;font-style:italic;">-- (all else should be 0)</span>
+         <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rii</span>
+         <span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">i</span><span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #000000;">1</span> <span style="color: #008080;">by</span> <span style="color: #0000FF;">-</span><span style="color: #000000;">1</span> <span style="color: #008080;">do</span>
+             <span style="color: #000000;">rj</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span>
+             <span style="color: #000000;">rji</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
+             <span style="color: #008080;">if</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">!=</span><span style="color: #000000;">0</span> <span style="color: #008080;">then</span>
+                 <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
+                 <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">-=</span> <span style="color: #000000;">rji</span><span style="color: #0000FF;">*</span><span style="color: #000000;">rii</span>
+                 <span style="color: #000000;">rj</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">+</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">0</span>
+                 <span style="color: #000000;">rules</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">rj</span>
+             <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
+         <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+     <span style="color: #008080;">return</span> <span style="color: #000000;">rules</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
+
+ <span style="color: #000080;font-style:italic;">-- Obviously these next two lines directly embody knowledge from the task, and
+ --  would need changing for an even slightly different version of the problem:</span>
+ <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">solveN</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rules</span><span style="color: #0000FF;">),</span>
+         <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">z</span> <span style="color: #000080;font-style:italic;">-- (as per task desc)</span>
+
+ <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"x=%d, y=%d, z=%d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">z</span><span style="color: #0000FF;">})</span>
+
+ <span style="color: #000080;font-style:italic;">-- finally evaluate all the equations and print it.</span>
+ <span style="color: #008080;">for</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
+     <span style="color: #008080;">for</span> <span style="color: #000000;">c</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">do</span>
+         <span style="color: #004080;">integer</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">k</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">l</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">m</span><span style="color: #0000FF;">}</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span>
+         <span style="color: #000000;">pyramid</span><span style="color: #0000FF;">[</span><span style="color: #000000;">r</span><span style="color: #0000FF;">][</span><span style="color: #000000;">c</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">k</span><span style="color: #0000FF;">+</span><span style="color: #000000;">l</span><span style="color: #0000FF;">*</span><span style="color: #000000;">x</span><span style="color: #0000FF;">+</span><span style="color: #000000;">m</span><span style="color: #0000FF;">*</span><span style="color: #000000;">z</span>
+     <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+ <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
+
+ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">pyramid</span><span style="color: #0000FF;">)</span>
+<!--
--- a/Task/Pascals-triangle-Puzzle/Phix/pascals-triangle-puzzle-2.phix
+++ b/Task/Pascals-triangle-Puzzle/Phix/pascals-triangle-puzzle-2.phix
@ -0,0 +1,27 @@
+(phixonline)-->
+ <span style="color: #0000FF;">?</span><span style="color: #000000;">solveN</span><span style="color: #0000FF;">({{</span><span style="color: #000000;">18</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">73</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">5</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}})</span> <span style="color: #000080;font-style:italic;">-- -- {5,13,8}</span>
+
+ <span style="color: #7060A8;">ppOpt</span><span style="color: #0000FF;">({</span><span style="color: #004600;">pp_Nest</span><span style="color: #0000FF;">,</span><span style="color: #000000;">0</span><span style="color: #0000FF;">})</span>
+ <span style="color: #000080;font-style:italic;">-- Or, hand-coding 11 simultaneous equations for 11 unknowns:
+ -- (be warned I had to reorder a bit to avoid rii==0 mishaps,
+ --  perhaps solveN() should find or even sort rules somehow)
+ --sequence pyramid = <nowiki>{{</nowiki>151},
+ --                  {"a","b"},
+ --                 {40,"c","d"},
+ --              {"e","f","g","h"},
+ --            {"x", 11,"y",  4,"z"<nowiki>}}</nowiki>
+ --               a  b  c  d  e  f  g  h  x  y  z</span>
+ <span style="color: #7060A8;">pp</span><span style="color: #0000FF;">(</span><span style="color: #000000;">solveN</span><span style="color: #0000FF;">({{</span><span style="color: #000000;">151</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- a+b=151</span>
+            <span style="color: #0000FF;">{</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- 40+c=a</span>
+            <span style="color: #0000FF;">{</span>  <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- c+d=b</span>
+            <span style="color: #0000FF;">{</span>  <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- g+h=d</span>
+            <span style="color: #0000FF;">{</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- e+f=40</span>
+            <span style="color: #0000FF;">{</span>  <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- f+g=c</span>
+            <span style="color: #0000FF;">{</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- x+11=e</span>
+            <span style="color: #0000FF;">{</span>  <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- y+4=g</span>
+            <span style="color: #0000FF;">{</span> <span style="color: #000000;">11</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- 11+y=f</span>
+            <span style="color: #0000FF;">{</span>  <span style="color: #000000;">4</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">},</span>  <span style="color: #000080;font-style:italic;">-- 4+z=h</span>
+            <span style="color: #0000FF;">{</span>  <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">0</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">1</span><span style="color: #0000FF;">,-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">}</span>   <span style="color: #000080;font-style:italic;">-- x+z=y
+ --        })) -- {81,70,41,29,16,24,17,12,5,13,8}</span>
+           <span style="color: #0000FF;">})[-</span><span style="color: #000000;">3</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">1</span><span style="color: #0000FF;">])</span> <span style="color: #000080;font-style:italic;">-- {5,13,8}</span>
+<!--
--- a/Task/Pascals-triangle-Puzzle/Phix/pascals-triangle-puzzle-3.phix
+++ b/Task/Pascals-triangle-Puzzle/Phix/pascals-triangle-puzzle-3.phix
@ -0,0 +1,4 @@
+(phixonline)-->
+ <span style="color: #004080;">integer</span> <span style="color: #000000;">Y</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">(</span><span style="color: #000000;">151</span><span style="color: #0000FF;">-</span><span style="color: #000000;">4</span><span style="color: #0000FF;">*(</span><span style="color: #000000;">11</span><span style="color: #0000FF;">+</span><span style="color: #000000;">4</span><span style="color: #0000FF;">))/</span><span style="color: #000000;">7</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">X</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">40</span><span style="color: #0000FF;">-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">*</span><span style="color: #000000;">11</span><span style="color: #0000FF;">-</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">Z</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">Y</span><span style="color: #0000FF;">-</span><span style="color: #000000;">X</span>
+ <span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"Two-liner: x=%d, y=%d, z=%d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">X</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Y</span><span style="color: #0000FF;">,</span><span style="color: #000000;">Z</span><span style="color: #0000FF;">})</span>
+<!--
--- a/Task/Pascals-triangle-Puzzle/Picat/pascals-triangle-puzzle-1.picat
+++ b/Task/Pascals-triangle-Puzzle/Picat/pascals-triangle-puzzle-1.picat
@ -0,0 +1,31 @@
+import cp.
+
+go =>
+   puzzle(T, X, Y,Z),
+   foreach(TT in T)
+     println(TT)
+   end,
+   println([x=X,y=Y,z=Z]),
+   nl,
+   fail, % are there any more solutions?
+   nl.
+
+% Port of the Prolog solution
+puzzle(Ts, X, Y, Z) :-
+    Ts =   [ [151],
+            [_, _],
+          [40, _, _],
+         [_, _, _, _],
+       [X, 11, Y, 4, Z]],
+    Y #= X + Z,
+    triangle(Ts),
+    Vs = vars(Ts),
+    Vs :: 0..10000,
+    solve(Vs).
+
+triangle([T|Ts]) :-
+  ( Ts = [N|_] -> triangle_(T, N), triangle(Ts) ; true ).
+
+triangle_([], _).
+triangle_([T|Ts],[A,B|Rest]) :-
+   T #= A + B, triangle_(Ts, [B|Rest]).
--- a/Task/Pascals-triangle-Puzzle/Picat/pascals-triangle-puzzle-2.picat
+++ b/Task/Pascals-triangle-Puzzle/Picat/pascals-triangle-puzzle-2.picat
@ -0,0 +1,48 @@
+import cp.
+
+puzzle2 =>
+  N = 5, % number of rows
+  Len = (N*(N+1)) div 2, % number of entries
+
+  % The triangle numbers for 1..N
+  T = [I*(I+1) div 2 : I in 1..N],
+
+  % The index of first number to use in addition
+  % create the indices of the numbers to add,
+  % i.e. Adds[I] + Adds[I+1]
+  Adds = new_list(T[N-1]),
+  Adds[1] := 2,
+  foreach(I in 2..T[N-1])
+    % "jump" of 2 when i-1 is a triangle number
+    if membchk(I-1,T) then
+      Adds[I] := Adds[I-1] + 2
+    else
+      Adds[I] := Adds[I-1] + 1
+    end
+  end,
+
+  % the pyramid
+  MaxVal = 10_000,
+  L = new_list(Len),
+  L :: 1..MaxVal,
+
+  % The clues.
+  L =    [   151,
+            _, _,
+            40, _, _,
+          _, _,_ , _ ,
+         X, 11, Y, 4, Z
+  ],
+
+  % The sums
+  foreach(I in 1..T[N-1])
+    L[I] #= L[Adds[I]]+L[Adds[I]+1]
+  end,
+
+  % The extra constraint
+  Y #= X + Z,
+
+  solve(L),
+  println([x=X,y=Y,z=Z]),
+  fail, % check if there is another solution
+  nl.
--- a/Task/Pascals-triangle-Puzzle/Picat/pascals-triangle-puzzle-3.picat
+++ b/Task/Pascals-triangle-Puzzle/Picat/pascals-triangle-puzzle-3.picat
@ -0,0 +1,33 @@
+import cp.
+
+puzzle3 =>
+  %       1
+  %      2  3
+  %    4  5  6
+  %  7  8  9  10
+  %11 12 13 14 15
+
+  X = new_list(15),
+  X :: 0..10_000,
+  X[1] #= X[2]+X[3],
+  X[2] #= X[4]+X[5],
+  X[3] #= X[5]+X[6],
+  X[4] #= X[7]+X[8],
+  X[5] #= X[8]+X[9],
+  X[6] #= X[9]+X[10],
+  X[7] #= X[11]+X[12],
+  X[8] #= X[12]+X[13],
+  X[9] #= X[13]+X[14],
+  X[10] #= X[14]+X[15],
+  X[13] #= X[11] + X[15], % Y=X+Z,
+
+  % The hints
+  X[1] #= 151,
+  X[4] #= 40,
+  X[12] #= 11,
+  X[14] #= 4,
+
+  solve(X),
+  println([x=X[11],y=X[13],z=X[15]]),
+  fail,
+  nl.
--- a/Task/Pascals-triangle-Puzzle/PicoLisp/pascals-triangle-puzzle.l
+++ b/Task/Pascals-triangle-Puzzle/PicoLisp/pascals-triangle-puzzle.l
@ -0,0 +1,44 @@
+(be number (@N @Max)
+   (^ @C (box 0))
+   (repeat)
+   (or
+      ((^ @ (>= (val (-> @C)) (-> @Max))) T (fail))
+      ((^ @N (inc (-> @C)))) ) )
+
+(be + (@A @B @Sum)
+   (^ @ (-> @A))
+   (^ @ (-> @B))
+   (^ @Sum (+ (-> @A) (-> @B))) )
+
+(be + (@A @B @Sum)
+   (^ @ (-> @A))
+   (^ @ (-> @Sum))
+   (^ @B (- (-> @Sum) (-> @A)))
+   T
+   (^ @ (ge0 (-> @B))) )
+
+(be + (@A @B @Sum)
+   (number @A @Sum)
+   (^ @B (- (-> @Sum) (-> @A))) )
+
+#{
+         151
+        A   B
+      40  C   D
+     E  F  G    H
+   X  11  Y   4   Z
+}#
+
+(be puzzle (@X @Y @Z)
+   (+ @A @B 151)
+   (+ 40 @C @A)
+   (+ @C @D @B)
+   (+ @E @F 40)
+   (+ @F @G @C)
+   (+ @G @H @D)
+   (+ @X 11 @E)
+   (+ 11 @Y @F)
+   (+ @Y 4 @G)
+   (+ 4 @Z @H)
+   (+ @X @Z @Y)
+   T )
--- a/Task/Pascals-triangle-Puzzle/Prolog/pascals-triangle-puzzle.pro
+++ b/Task/Pascals-triangle-Puzzle/Prolog/pascals-triangle-puzzle.pro
@ -0,0 +1,19 @@
+:- use_module(library(clpfd)).
+
+puzzle(Ts, X, Y, Z) :-
+    Ts =   [ [151],
+            [_, _],
+          [40, _, _],
+         [_, _, _, _],
+       [X, 11, Y, 4, Z]],
+    Y #= X + Z, triangle(Ts), append(Ts, Vs), Vs ins 0..sup, label(Vs).
+
+triangle([T|Ts]) :- ( Ts = [N|_] -> triangle_(T, N), triangle(Ts) ; true ).
+
+triangle_([], _).
+triangle_([T|Ts], [A,B|Rest]) :- T #= A + B, triangle_(Ts, [B|Rest]).
+
+% ?- puzzle(_,X,Y,Z).
+% X = 5,
+% Y = 13,
+% Z = 8 ;
--- a/Task/Pascals-triangle-Puzzle/PureBasic/pascals-triangle-puzzle.basic
+++ b/Task/Pascals-triangle-Puzzle/PureBasic/pascals-triangle-puzzle.basic
@ -0,0 +1,31 @@
+; Known;
+; A.
+;         [ 151]
+;        [a ][b ]
+;      [40][c ][d ]
+;    [e ][f ][g ][h ]
+;  [ X][11][ Y][ 4][ Z]
+;
+; B.
+;  Y = X + Z
+
+Procedure.i SolveForZ(x)
+  Protected a,b,c,d,e,f,g,h,z
+  For z=0 To 20
+    e=x+11: f=11+(x+z): g=(x+z)+4: h=4+z
+    If e+f=40
+      c=f+g : d=g+h: a=40+c: b=c+d
+      If a+b=151
+        ProcedureReturn z
+      EndIf
+    EndIf
+  Next z
+  ProcedureReturn -1
+EndProcedure
+
+Define x=-1, z=0, title$="Pascal's triangle/Puzzle in PureBasic"
+Repeat
+  x+1
+  z=SolveForZ(x)
+Until z>=0
+MessageRequester(title$,"X="+Str(x)+#CRLF$+"Y="+Str(x+z)+#CRLF$+"Z="+Str(z))
--- a/Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-1.py
+++ b/Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-1.py
@ -0,0 +1,122 @@
+# Pyramid solver
+#            [151]
+#         [   ] [   ]
+#      [ 40] [   ] [   ]
+#   [   ] [   ] [   ] [   ]
+#[ X ] [ 11] [ Y ] [ 4 ] [ Z ]
+#  X -Y + Z = 0
+
+def combine( snl, snr ):
+
+	cl = {}
+	if isinstance(snl, int):
+		cl['1'] = snl
+	elif isinstance(snl, string):
+		cl[snl] = 1
+	else:
+		cl.update( snl)
+
+	if isinstance(snr, int):
+		n = cl.get('1', 0)
+		cl['1'] = n + snr
+	elif isinstance(snr, string):
+		n = cl.get(snr, 0)
+		cl[snr] = n + 1
+	else:
+		for k,v in snr.items():
+			n = cl.get(k, 0)
+			cl[k] = n+v
+	return cl
+
+
+def constrain(nsum, vn ):
+	nn = {}
+	nn.update(vn)
+	n = nn.get('1', 0)
+	nn['1'] = n - nsum
+	return nn
+
+def makeMatrix( constraints ):
+	vmap = set()
+	for c in constraints:
+		vmap.update( c.keys())
+	vmap.remove('1')
+	nvars = len(vmap)
+	vmap = sorted(vmap)		# sort here so output is in sorted order
+	mtx = []
+	for c in constraints:
+		row = []
+		for vv in vmap:
+			row.append(float(c.get(vv, 0)))
+		row.append(-float(c.get('1',0)))
+		mtx.append(row)
+	
+	if len(constraints) == nvars:
+		print 'System appears solvable'
+	elif len(constraints) < nvars:
+		print 'System is not solvable - needs more constraints.'
+	return mtx, vmap
+
+
+def SolvePyramid( vl, cnstr ):
+
+	vl.reverse()
+	constraints = [cnstr]
+	lvls = len(vl)
+	for lvln in range(1,lvls):
+		lvd = vl[lvln]
+		for k in range(lvls - lvln):
+			sn = lvd[k]
+			ll = vl[lvln-1]
+			vn = combine(ll[k], ll[k+1])
+			if sn is None:
+				lvd[k] = vn
+			else:
+				constraints.append(constrain( sn, vn ))
+
+	print 'Constraint Equations:'
+	for cstr in constraints:
+		fset = ('%d*%s'%(v,k) for k,v in cstr.items() )
+		print ' + '.join(fset), ' = 0'
+
+	mtx,vmap = makeMatrix(constraints)
+
+	MtxSolve(mtx)
+
+	d = len(vmap)
+	for j in range(d):
+		print vmap[j],'=', mtx[j][d]
+
+
+def MtxSolve(mtx):
+	# Simple Matrix solver...
+
+	mDim = len(mtx)			# dimension---
+	for j in range(mDim):
+		rw0= mtx[j]
+		f = 1.0/rw0[j]
+		for k in range(j, mDim+1):
+			rw0[k] *= f
+		
+		for l in range(1+j,mDim):
+			rwl = mtx[l]
+			f = -rwl[j]
+			for k in range(j, mDim+1):
+				rwl[k] += f * rw0[k]
+
+	# backsolve part ---
+	for j1 in range(1,mDim):
+		j = mDim - j1
+		rw0= mtx[j]
+		for l in range(0, j):
+			rwl = mtx[l]
+			f = -rwl[j]
+			rwl[j]    += f * rw0[j]
+			rwl[mDim] += f * rw0[mDim]
+
+	return mtx
+
+
+p = [ [151], [None,None], [40,None,None], [None,None,None,None], ['X', 11, 'Y', 4, 'Z'] ]
+addlConstraint = { 'X':1, 'Y':-1, 'Z':1, '1':0 }
+SolvePyramid( p, addlConstraint)
--- a/Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-2.py
+++ b/Task/Pascals-triangle-Puzzle/Python/pascals-triangle-puzzle-2.py
@ -0,0 +1,19 @@
+from csp import Problem
+
+p = Problem()
+pvars = "R2 R3 R5 R6 R7 R8 R9 R10 X Y Z".split()
+# 0-151 is the possible finite range of the variables
+p.addvars(pvars, xrange(152))
+p.addrule("R7 == X + 11")
+p.addrule("R8 == Y + 11")
+p.addrule("R9 == Y + 4")
+p.addrule("R10 == Z + 4")
+p.addrule("R7 + R8 == 40")
+p.addrule("R5 == R8 + R9")
+p.addrule("R6 == R9 + R10")
+p.addrule("R2 == 40 + R5")
+p.addrule("R3 == R5 + R6")
+p.addrule("R2 + R3 == 151")
+p.addrule("Y == X + Z")
+for sol in p.xsolutions():
+    print [sol[k] for k in "XYZ"]
--- a/Task/Pascals-triangle-Puzzle/REXX/pascals-triangle-puzzle.rexx
+++ b/Task/Pascals-triangle-Puzzle/REXX/pascals-triangle-puzzle.rexx
@ -0,0 +1,32 @@
+/*REXX program solves a   (Pascal's)   "Pyramid of Numbers"   puzzle given four values. */
+      /* ╔══════════════════════════════════════════════════╗
+         ║                             answer               ║
+         ║                            /                     ║
+         ║              mid          /                      ║
+         ║                 \       151                      ║
+         ║                  \   ααα   ααα                   ║
+         ║                   40    ααα   ααα                ║
+         ║               ααα   ααα   ααα   ααα              ║
+         ║              x    11     y     4     z           ║
+         ║                  /              \                ║
+         ║ find:           /                \               ║
+         ║ x y z          b                  d              ║
+         ╚══════════════════════════════════════════════════╝ */
+   do #=2;     _= sourceLine(#);  n= pos('_', _) /* [↓]  this DO loop shows (above) box.*/
+   if n\==0  then leave;             say _       /*only display  up to  the above line. */
+   end   /*#*/;                      say         /* [↑]  this is a way for in─line doc. */
+parse arg  b  d  mid  answer  .                  /*obtain optional variables from the CL*/
+if     b=='' |      b==","  then      b=  11     /*Not specified?  Then use the default.*/
+if     d=='' |      d==","  then      d=   4     /* "      "         "   "   "     "    */
+if    mid='' |    mid==","  then    mid=  40     /* "      "         "   "   "     "    */
+if answer='' | answer==","  then answer= 151     /* "      "         "   "   "     "    */
+                      big= answer - 4*b - 4*d    /*calculate  BIG  number less constants*/
+   do      x=-big  to big
+     do    y=-big  to big
+     if x+y\==mid - 2*b  then iterate            /*40 = x+2B+Y   ──or──   40-2*11 = x+y */
+        do z=-big  to big
+        if z \== y - x   then iterate            /*Z  has to equal   Y-X       (Y= X+Z) */
+        if x+y*6+z==big  then say right('x =', n)  x  right("y =",n)  y  right('z =',n)  z
+        end   /*z*/
+     end      /*y*/
+   end        /*x*/                              /*stick a fork in it,  we're all done. */
--- a/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-1.rkt
+++ b/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-1.rkt
@ -0,0 +1,14 @@
+#lang racket/base
+(require racket/list)
+
+(struct cell (v x z) #:transparent)
+
+(define (cell-add cx cy)
+  (cell (+ (cell-v cx) (cell-v cy))
+        (+ (cell-x cx) (cell-x cy))
+        (+ (cell-z cx) (cell-z cy))))
+
+(define (cell-sub cx cy)
+  (cell (- (cell-v cx) (cell-v cy))
+        (- (cell-x cx) (cell-x cy))
+        (- (cell-z cx) (cell-z cy))))
--- a/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-2.rkt
+++ b/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-2.rkt
@ -0,0 +1,7 @@
+(define (row-above row) (map cell-add (drop row 1) (drop-right row 1)))
+
+(define row0 (list (cell 0 1 0) (cell 11 0 0) (cell 0 1 1) (cell 4 0 0) (cell 0 0 1)))
+(define row1 (row-above row0))
+(define row2 (row-above row1))
+(define row3 (row-above row2))
+(define row4 (row-above row3))
--- a/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-3.rkt
+++ b/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-3.rkt
@ -0,0 +1,2 @@
+(define eqn40 (cell-sub (car row4) (cell 151 0 0)))
+(define eqn20 (cell-sub (car row2) (cell 40 0 0)))
--- a/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-4.rkt
+++ b/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-4.rkt
@ -0,0 +1,6 @@
+(define (det2 eqnx eqny get-one get-oth)
+  (- (* (get-one eqnx) (get-oth eqny)) (* (get-one eqny) (get-oth eqnx))))
+
+(define (cramer2 eqnx eqny get-val get-unk get-oth)
+  (/ (det2 eqnx eqny get-val get-oth)
+     (det2 eqnx eqny get-unk get-oth)))
--- a/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-5.rkt
+++ b/Task/Pascals-triangle-Puzzle/Racket/pascals-triangle-puzzle-5.rkt
@ -0,0 +1,6 @@
+(define x (- (cramer2 eqn20 eqn40 cell-v cell-x cell-z)))
+(define z (- (cramer2 eqn20 eqn40 cell-v cell-z cell-x)))
+
+(displayln (list "X" x))
+(displayln (list "Y" (+ x z)))
+(displayln (list "Z" z))
--- a/Task/Pascals-triangle-Puzzle/Raku/pascals-triangle-puzzle.raku
+++ b/Task/Pascals-triangle-Puzzle/Raku/pascals-triangle-puzzle.raku
@ -0,0 +1,43 @@
+# set up triangle
+my $rows = 5;
+my @tri = (1..$rows).map: { [ { x => 0, z => 0, v => 0, rhs => Nil } xx $_ ] }
+@tri[0][0]<rhs> = 151;
+@tri[2][0]<rhs> = 40;
+@tri[4][0]<x> = 1;
+@tri[4][1]<v> = 11;
+@tri[4][2]<x> = 1;
+@tri[4][2]<z> = 1;
+@tri[4][3]<v> = 4;
+@tri[4][4]<z> = 1;
+
+# aggregate from bottom to top
+for @tri - 2 ... 0 -> $row {
+    for 0 ..^ @tri[$row] -> $col {
+        @tri[$row][$col]{$_} = @tri[$row+1][$col]{$_} + @tri[$row+1][$col+1]{$_} for 'x','z','v';
+    }
+}
+
+# find equations
+my @eqn = gather for @tri -> $row {
+    for @$row -> $cell {
+        take [ $cell<x>, $cell<z>, $cell<rhs> - $cell<v> ] if defined $cell<rhs>;
+    }
+}
+
+# print equations
+say "Equations:";
+say "  x +   z = y";
+for @eqn -> [$x,$z,$y] { say "$x x + $z z = $y" }
+
+# solve
+my $f = @eqn[0][1] / @eqn[1][1];
+@eqn[0][$_] -=  $f * @eqn[1][$_] for 0..2;
+$f = @eqn[1][0] / @eqn[0][0];
+@eqn[1][$_] -=  $f * @eqn[0][$_] for 0..2;
+
+# print solution
+say "Solution:";
+my $x = @eqn[0][2] / @eqn[0][0];
+my $z = @eqn[1][2] / @eqn[1][1];
+my $y = $x + $z;
+say "x=$x, y=$y, z=$z";
--- a/Task/Pascals-triangle-Puzzle/Ruby/pascals-triangle-puzzle.rb
+++ b/Task/Pascals-triangle-Puzzle/Ruby/pascals-triangle-puzzle.rb
@ -0,0 +1,62 @@
+require 'rref'
+
+pyramid = [
+           [ 151],
+          [nil,nil],
+        [40,nil,nil],
+      [nil,nil,nil,nil],
+    ["x", 11,"y", 4,"z"]
+]
+pyramid.each{|row| p row}
+
+equations = [[1,-1,1,0]]   # y = x + z
+
+def parse_equation(str)
+  eqn = [0] * 4
+  lhs, rhs = str.split("=")
+  eqn[3] = rhs.to_i
+  for term in lhs.split("+")
+    case term
+    when "x" then eqn[0] += 1
+    when "y" then eqn[1] += 1
+    when "z" then eqn[2] += 1
+    else          eqn[3] -= term.to_i
+    end
+  end
+  eqn
+end
+
+-2.downto(-5) do |row|
+  pyramid[row].each_index do |col|
+    val = pyramid[row][col]
+    sum = "%s+%s" % [pyramid[row+1][col], pyramid[row+1][col+1]]
+    if val.nil?
+      pyramid[row][col] = sum
+    else
+      equations << parse_equation(sum + "=#{val}")
+    end
+  end
+end
+
+reduced = convert_to(reduced_row_echelon_form(equations), :to_i)
+
+for eqn in reduced
+  if eqn[0] + eqn[1] + eqn[2] != 1
+    fail "no unique solution! #{equations.inspect} ==> #{reduced.inspect}"
+  elsif eqn[0] == 1 then x = eqn[3]
+  elsif eqn[1] == 1 then y = eqn[3]
+  elsif eqn[2] == 1 then z = eqn[3]
+  end
+end
+
+puts
+puts "x == #{x}"
+puts "y == #{y}"
+puts "z == #{z}"
+
+answer = []
+for row in pyramid
+  answer << row.collect {|cell| eval cell.to_s}
+end
+puts
+answer.each{|row| p row}
--- a/Task/Pascals-triangle-Puzzle/Scala/pascals-triangle-puzzle.scala
+++ b/Task/Pascals-triangle-Puzzle/Scala/pascals-triangle-puzzle.scala
@ -0,0 +1,12 @@
+object PascalTriangle extends App {
+
+  val (x, y, z) = pascal(11, 4, 40, 151)
+
+  def pascal(a: Int, b: Int, mid: Int, top: Int): (Int, Int, Int) = {
+    val y = (top - 4 * (a + b)) / 7
+    val x = mid - 2 * a - y
+    (x, y, y - x)
+  }
+
+  println(if (x != 0) s"Solution is: x = $x, y = $y, z = $z" else "There is no solution.")
+}
--- a/Task/Pascals-triangle-Puzzle/Sidef/pascals-triangle-puzzle.sidef
+++ b/Task/Pascals-triangle-Puzzle/Sidef/pascals-triangle-puzzle.sidef
@ -0,0 +1,47 @@
+# set up triangle
+var rows = 5
+var tri = rows.of {|i| (i+1).of { Hash(x => 0, z => 0, v => 0, rhs => nil) } }
+tri[0][0]{:rhs} = 151
+tri[2][0]{:rhs} = 40
+tri[4][0]{:x} = 1
+tri[4][1]{:v} = 11
+tri[4][2]{:x} = 1
+tri[4][2]{:z} = 1
+tri[4][3]{:v} = 4
+tri[4][4]{:z} = 1
+ 
+# aggregate from bottom to top
+for row in (tri.len ^.. 1) {
+    for col in (^tri[row-1]) {
+        [:x, :z, :v].each { |key|
+            tri[row-1][col]{key} = (tri[row][col]{key} + tri[row][col+1]{key})
+        }
+    }
+}
+ 
+# find equations
+var eqn = gather {
+    for r in tri {
+        for c in r {
+            take([c{:x}, c{:z}, c{:rhs} - c{:v}]) if defined(c{:rhs})
+        }
+    }
+}
+ 
+# print equations
+say "Equations:"
+say " x +  z = y"
+for x,z,y in eqn { say "#{x}x + #{z}z = #{y}" }
+ 
+# solve
+var f = (eqn[0][1] / eqn[1][1])
+{|i| eqn[0][i] -= (f * eqn[1][i]) } << ^3
+f = (eqn[1][0] / eqn[0][0])
+{|i| eqn[1][i] -= (f * eqn[0][i]) } << ^3
+ 
+# print solution
+say "Solution:"
+var x = (eqn[0][2] / eqn[0][0])
+var z = (eqn[1][2] / eqn[1][1])
+var y = (x + z)
+say "x=#{x}, y=#{y}, z=#{z}"
--- a/Task/Pascals-triangle-Puzzle/SystemVerilog/pascals-triangle-puzzle.v
+++ b/Task/Pascals-triangle-Puzzle/SystemVerilog/pascals-triangle-puzzle.v
@ -0,0 +1,38 @@
+program main;
+
+  class Triangle;
+    rand bit [7:0] a,b,c,d,e,f,g,h,X,Y,Z;
+
+    function new();
+      randomize;
+      $display("     [%0d]",                151);
+      $display("    [%0d][%0d]",            a, b);
+      $display("   [%0d][%0d][%0d]",        40,c,d);
+      $display("  [%0d][%0d][%0d][%0d]",    e,f,g,h);
+      $display(" [%0d][%0d][%0d][%0d][%0d]",X,11,Y,4,Z);
+    endfunction
+
+    constraint structure {
+       151 == a + b;
+
+         a == 40 + c;
+         b == c + d;
+
+        40 == e + f;
+         c == f + g;
+         d == g + h;
+
+         e == X + 11;
+         f == 11 + Y;
+         g == Y + 4;
+         h == 4 + Z;
+    };
+
+    constraint extra {
+         Y == X + Z;
+    };
+
+  endclass
+
+  Triangle answer = new;
+endprogram
--- a/Task/Pascals-triangle-Puzzle/Tcl/pascals-triangle-puzzle.tcl
+++ b/Task/Pascals-triangle-Puzzle/Tcl/pascals-triangle-puzzle.tcl
@ -0,0 +1,68 @@
+package require Tcl 8.5
+namespace path ::tcl::mathop
+
+set pyramid {
+    {151.0 "" "" "" ""}
+    {"" "" "" "" ""}
+    {40.0 "" "" "" ""}
+    {"" "" "" "" ""}
+    {x 11.0 y 4.0 z}
+}
+
+set equations {{1 -1 1 0}}
+
+proc simplify {terms val} {
+    set vars {0 0 0}
+    set x 0
+    set y 1
+    set z 2
+    foreach term $terms {
+        switch -exact -- $term {
+            x - y - z {
+                lset vars [set $term] [+ 1 [lindex $vars [set $term]]]
+            }
+            default {
+                set val [- $val $term]
+            }
+        }
+    }
+    return [concat $vars $val]
+}
+
+for {set row [+ [llength $pyramid] -2]} {$row >= 0} {incr row -1} {
+    for {set cell 0} {$cell <= $row} {incr cell } {
+	set sum [concat [lindex $pyramid [+ 1 $row] $cell] [lindex $pyramid [+ 1 $row] [+ 1 $cell]]]
+	if {[set val [lindex $pyramid $row $cell]] ne ""} {
+            lappend equations [simplify $sum $val]
+	} else {
+            lset pyramid $row $cell  $sum
+        }
+    }
+}
+
+set solution [toRREF $equations]
+foreach row $solution {
+    lassign $row a b c d
+    if {$a + $b + $c > 1} {
+        error "problem does not have a unique solution"
+    }
+    if {$a} {set x $d}
+    if {$b} {set y $d}
+    if {$c} {set z $d}
+}
+puts "x=$x"
+puts "y=$y"
+puts "z=$z"
+
+foreach row $pyramid {
+    set newrow {}
+    foreach cell $row {
+        if {$cell eq ""} {
+            lappend newrow ""
+        } else {
+            lappend newrow [expr [join [string map [list x $x y $y z $z] $cell] +]]
+        }
+    }
+    lappend solved $newrow
+}
+print_matrix $solved
--- a/Task/Pascals-triangle-Puzzle/Wren/pascals-triangle-puzzle.wren
+++ b/Task/Pascals-triangle-Puzzle/Wren/pascals-triangle-puzzle.wren
@ -0,0 +1,18 @@
+import "/fmt" for Fmt
+
+var isIntegral = Fn.new { |x, tol| x.fraction.abs <= tol }
+
+var pascal = Fn.new { |a, b, mid, top|
+    var yd = (top - 4 * (a + b)) / 7
+    if (!isIntegral.call(yd, 0.0001)) return [0, 0, 0]
+    var y = yd.truncate
+    var x = mid - 2*a - y
+    return [x, y, y - x]
+}
+
+var sol = pascal.call(11, 4, 40, 151)
+if (sol[0] != 0) {
+    Fmt.print("Solution is: x = $d, y = $d, z = $d", sol[0], sol[1], sol[2])
+} else {
+    System.print("There is no solution")
+}
--- a/Task/Pascals-triangle-Puzzle/XPL0/pascals-triangle-puzzle.xpl0
+++ b/Task/Pascals-triangle-Puzzle/XPL0/pascals-triangle-puzzle.xpl0
@ -0,0 +1,34 @@
+proc Print; int N, A, B, C, D, E;
+int  I, P;
+def  Tab = $09;
+[P:= @A;        \point to first number
+for I:= N to 5-1 do ChOut(0, Tab);
+for I:= 0 to N-1 do
+    [IntOut(0, P(I));  ChOut(0, Tab);  ChOut(0, Tab)];
+CrLf(0);
+];
+
+int N, P, Q, R, S, T, U, V, W, X, Y, Z; \       151
+[for X:= 0 to 40-11 do                  \      N   P
+    for Z:= 0 to 151-4 do               \    Q   R   S
+        [Y:= X+Z;                       \  T   U   V   W
+        T:= X+11;                       \X   11  Y   4   Z
+        U:= 11+Y;
+        V:= Y+4;
+        W:= 4+Z;
+        if T+U = 40 then
+            [R:= U+V;
+            S:= V+W;
+            N:= 40+R;
+            P:= R+S;
+            if N+P = 151 then
+                [Print(1, 151);
+                 Print(2, N, P);
+                 Print(3, 40, R, S);
+                 Print(4, T, U, V, W);
+                 Print(5, X, 11, Y, 4, Z);
+                 exit;
+                ];
+            ];
+        ];
+]
--- a/Task/Pascals-triangle-Puzzle/Zkl/pascals-triangle-puzzle-1.zkl
+++ b/Task/Pascals-triangle-Puzzle/Zkl/pascals-triangle-puzzle-1.zkl
@ -0,0 +1,12 @@
+# Pyramid solver
+#            [151]
+#         [   ] [   ]
+#      [ 40] [   ] [   ]
+#   [   ] [   ] [   ] [   ]
+#[ X ] [ 11] [ Y ] [ 4 ] [ Z ]
+# Known: X - Y + Z = 0
+
+p:=T( L(151), L(Void,Void), L(40,Void,Void), L(Void,Void,Void,Void),
+      L("X", 11, "Y", 4, "Z") );
+addlConstraint:=Dictionary( "X",1, "Y",-1, "Z",1, "1",0 );
+solvePyramid(p, addlConstraint);
--- a/Task/Pascals-triangle-Puzzle/Zkl/pascals-triangle-puzzle-2.zkl
+++ b/Task/Pascals-triangle-Puzzle/Zkl/pascals-triangle-puzzle-2.zkl
@ -0,0 +1,83 @@
+fcn solvePyramid([List]vl,[Dictionary]cnstr){  //ListOfLists,Hash-->zip
+   vl=vl.reverse();
+   constraints:=L(cnstr);
+   lvls:=vl.len();
+   foreach lvln in ([1..lvls-1]){
+      lvd:=vl[lvln];
+      foreach k in (lvls-lvln){
+         sn:=lvd[k];
+	 ll:=vl[lvln-1];
+	 vn:=combine(ll[k], ll[k+1]);
+	 if(Void==sn) lvd[k]=vn;
+	 else constraints.append(constrainK(sn,vn));
+      }
+   }
+   println("Constraint Equations:");
+   constraints.pump(Console.println,fcn(hash){
+      hash.pump(List,fcn([(k,v)]){"%d*%s".fmt(v,k)}).concat(" + ") + " = 0"
+   });
+
+   mtx,vmap:=makeMatrix(constraints);
+   mtxSolve(mtx);
+
+   d:=vmap.len();
+   foreach j in (d){ println(vmap[j]," = ", mtx[j][d]); }
+}
+
+fcn [mixin=Dictionary] constrainK([Int]nsum,[Dictionary]vn){ //-->new hash of old hash, sum K
+   nn:=vn.copy(); nn["1"]=nn.find("1",0) - nsum;
+   return(nn.makeReadOnly());
+}
+
+fcn combine(snl,snr){ //Int|String|Hash *2 --> new Hash
+   cl:=Dictionary();
+   if(snl.isInstanceOf(Int))         cl["1"]=snl;
+   else if(snl.isInstanceOf(String)) cl[snl]=1;
+   else				     cl     =snl.copy();
+
+   if(snr.isInstanceOf(Int))         cl["1"]=cl.find("1",0) + snr;
+   else if(snr.isInstanceOf(String)) cl[snr]=cl.find(snr,0) + 1;
+   else{ foreach k,v in (snr){ 	     cl[k]  =cl.find(k,0)   + v; } }
+   return(cl.makeReadOnly())
+}
+
+    //-->(listMatrix(row(X,Y,Z,c),row...),List("X","Y","Z"))
+fcn makeMatrix([Dictionary]constraints){
+   vmap:=Dictionary();// create a sorted list of the variable names in constraints
+   foreach c in (constraints){ vmap.extend(c) }  // no duplicate names
+   vmap.del("1"); vmap=vmap.keys.sort();  # sort here so output is in sorted order
+
+   mtx:=constraints.pump(List,'wrap(c){ // create list of [writeable] rows
+      vmap.pump(List, c.find.fp1(0),"toFloat").copy()
+      .append(-c.find("1",0).toFloat())
+   }).copy();
+
+   nvars:=vmap.len();
+   if(constraints.len()==nvars) println("System appears solvable");
+   else if(constraints.len()<nvars)
+      println("System is not solvable - needs more constraints.");
+   return(mtx,vmap);
+}
+
+fcn mtxSolve([List]mtx){ //munge mtx	# Simple Matrix solver...
+   mDim:=mtx.len();			# num rows
+   foreach j in (mDim){
+      rw0:=mtx[j];
+      f:=1.0/rw0[j];
+      foreach k in ([j..mDim]){ rw0[k]=rw0[k]*f }
+      foreach l in ([j+1..mDim-1]){
+         rwl:=mtx[l]; f:=-rwl[j];
+	 foreach k in ([j..mDim]){ rwl[k]+=f*rw0[k] }
+      }
+   }
+   # backsolve part ---
+   foreach j1 in ([1..mDim-1]){
+      j:=mDim - j1; rw0:=mtx[j];
+      foreach l in (j){
+	 rwl:=mtx[l]; f:=-rwl[j];
+	 rwl[j]   +=f*rw0[j];
+	 rwl[mDim]+=f*rw0[mDim];
+      }
+   }
+   return(mtx);
+}
				`@ -0,0 +1 @@`
				`puzzle = [["151"],["",""],["40","",""],["","","",""],["X","11","Y","4","Z"]]`
				`@ -0,0 +1 @@`
				`\|."2(#~chk"2) 2(+/\)^:(<ord)"1 base/"1>,{ ;~i:28`
				`@ -0,0 +1 @@`
				`,.(1+i.5)<@{."0 1{.\|."2(#~chk"2) 2(+/\)^:(<ord)"1 base/"1>,{ ;~i:28`
				`@ -0,0 +1 @@`
				`,.(<@{."0 1~1+i.@#){.\|."2(#~chk"2) 2(+/\)^:(<ord)"1 base/"1>,{ ;~i:28`
				`@ -0,0 +1 @@`
				`{{b -> 81, c -> 70, e -> 41, f -> 29, g -> 16, h -> 24, i -> 17, j -> 12, X -> 5, Y -> 13, Z -> 8}}`