Add tasks for all the new languages

Task/Digital-root-Multiplicative-digital-root/Nim/digital-root-multiplicative-digital-root.nim

@@ -0,0 +1,28 @@
+import strutils, future
+
+template newSeqWith(len: int, init: expr): expr =
+  var result {.gensym.} = newSeq[type(init)](len)
+  for i in 0 .. <len:
+    result[i] = init
+  result
+
+proc mdroot(n): tuple[mp, mdr: int] =
+  var mdr = @[n]
+  while mdr[mdr.high] > 9:
+    var n = 1
+    for dig in $mdr[mdr.high]:
+      n *= parseInt($dig)
+    mdr.add n
+  (mdr.high, mdr[mdr.high])
+
+for n in [123321, 7739, 893, 899998]:
+  echo align($n, 6)," ",mdroot(n)
+echo ""
+
+var table = newSeqWith(10, newSeq[int]())
+for n in 0..int.high:
+  if table.map((x: seq[int]) => x.len).min >= 5: break
+  table[mdroot(n).mdr].add n
+
+for mp, val in table:
+  echo mp,": ",val[0..4]

Task/Digital-root-Multiplicative-digital-root/Sidef/digital-root-multiplicative-digital-root.sidef

@@ -0,0 +1,23 @@
+func mdroot(n) {
+  var (mdr, persist) = (n, 0)
+  while (mdr >= 10) {
+    mdr = mdr.digits.product
+    ++persist
+  }
+  [mdr, persist]
+}
+
+say "Number: MDR  MP\n======  ===  =="
+[123321, 7739, 893, 899998].each{|n| "%6d: %3d %3d\n" \
+                           .printf(n, mdroot(n)...) }
+
+var counter = Hash()
+
+Inf.times { |i|
+  var j = i-1
+  counter{mdroot(j).first} := [] << j
+  break if counter.values.all {|v| v.len >= 5 }
+}
+
+say "\nMDR: [n0..n4]\n===  ========"
+10.times {|i| "%3d: %s\n".printf(i-1, counter{i-1}.first(5)) }

Task/Digital-root-Multiplicative-digital-root/jq/digital-root-multiplicative-digital-root-1.jq

@@ -0,0 +1,32 @@
+def do_until(condition; next):
+  def u: if condition then . else (next|u) end;
+  u;
+
+def mdroot(n):
+  def multiply: reduce .[] as $i (1; .*$i);
+  # state: [mdr, persist]
+  [n, 0]
+  | do_until( .[0] < 10;
+              [(.[0] | tostring | explode | map(.-48) | multiply), .[1] + 1]
+            );
+
+# Produce a table with 10 rows (numbered from 0),
+# showing the first n numbers having the row-number as the mdr
+def tabulate(n):
+  # state: [answer_matrix, next_i]
+  def tab:
+    def minlength: map(length) | min;
+    .[0] as $matrix
+    | .[1] as $i
+    | if (.[0]|minlength) == n then .[0]
+      else (mdroot($i) | .[0]) as $mdr
+      | if $matrix[$mdr]|length < n then
+          ($matrix[$mdr] + [$i]) as $row
+          | $matrix | setpath([$mdr]; $row)
+        else $matrix
+        end
+      | [ ., $i + 1 ]
+      | tab
+      end;
+
+  [[], 0]  | tab;

Task/Digital-root-Multiplicative-digital-root/jq/digital-root-multiplicative-digital-root-2.jq

@@ -0,0 +1,15 @@
+def neatly:
+  . as $in
+  | range(0;length)
+  | "\(.): \($in[.])";
+
+def rjust(n): tostring | (n-length)*" " + .;
+
+# The task:
+"  i   : [MDR, MP]",
+((123321, 7739, 893, 899998) as $i
+ | "\($i|rjust(6)): \(mdroot($i))"),
+"",
+"Tabulation",
+"MDR: [n0..n4]",
+(tabulate(5) | neatly)

Task/Digital-root-Multiplicative-digital-root/jq/digital-root-multiplicative-digital-root-3.jq

@@ -0,0 +1,20 @@
+$ jq -n -r -c -f mdr.jq
+
+  i   : [MDR, MP]
+123321: [8,3]
+  7739: [8,3]
+   893: [2,3]
+899998: [0,2]
+
+Tabulation
+MDR: [n0..n4]
+0: [0,10,20,25,30]
+1: [1,11,111,1111,11111]
+2: [2,12,21,26,34]
+3: [3,13,31,113,131]
+4: [4,14,22,27,39]
+5: [5,15,35,51,53]
+6: [6,16,23,28,32]
+7: [7,17,71,117,171]
+8: [8,18,24,29,36]
+9: [9,19,33,91,119]