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Task/Pascals-triangle-Puzzle/Nim/pascals-triangle-puzzle.nim

@@ -0,0 +1,66 @@
+import math, strutils
+
+var B_X, B_Y, B_Z : int = 0
+
+type
+   Block_Value = object
+      Known   : int
+      X, Y, Z : int
+
+let
+   X: Block_Value = Block_Value(Known:0, X:1, Y:0, Z:0)
+   Y: Block_Value = Block_Value(Known:0, X:0, Y:1, Z:0)
+   Z: Block_Value = Block_Value(Known:0, X:0, Y:0, Z:1)
+
+proc Add (L : var Block_Value, R : Block_Value) =
+   # 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
+
+proc Add (L: var Block_Value, R: int) =
+   # Symbolically adds a value to the block
+   L.Known = L.Known + R
+
+proc Image (N : Block_Value): string =
+   # The block value, when X,Y,Z are known
+   result = $(N.Known + N.X * B_X + N.Y * B_Y + N.Z * B_Z)
+
+proc Solve_2x2 (A11: int, A12:int, B1:int, A21:int, A22:int, B2: int) =
+   # Don't care about things, supposing an integer solution exists
+   if A22 == 0:
+      B_X = toInt(B2 / A21)
+      B_Y = toInt((B1 - (A11*B_X)) / A12)
+   else:
+      B_X = toInt((B1*A22 - B2*A12) / (A11*A22 - A21*A12))
+      B_Y = toInt((B1 - A11*B_X) / A12)
+   B_Z = B_Y - B_X
+
+var B : array [1..5, array[1..5, Block_Value]]   # The lower triangle contains blocks
+
+# 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 countdown(4,1):
+   for Column in 1 .. Row:
+      Add (B[Row][Column], B[Row + 1][Column])
+      Add (B[Row][Column], B[Row + 1][Column + 1])
+
+# 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:
+   writeln(stdout,"")
+   for Column in 1..Row:
+      write(stdout, Image(B[Row][Column]), " ")

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.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.end -> downto(1)) {
+    for col in (tri[row-1].range) {
+        [: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]);
+for i in (0..2) { eqn[0][i] -= (f * eqn[1][i]) }
+f = (eqn[1][0] / eqn[0][0]);
+for i in (0..2) { eqn[1][i] -= (f * eqn[0][i]) }
+
+# 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}";