S2T2

Jim Randell 11:16 am on 2 January 2026 Permalink Reply
Tags: by: Graham Smithers ( 82 )   

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  Jim Randell 11:17 am on 2 January 2026 Permalink | Reply

  Here is a solution using the [[ SubstitutedExpression ]] solver from the enigma.py library:

  It runs in 85ms. (Internal runtime of the generated code is 8.8ms).

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  "div(GHIJ, DEF) < 10"
  "div(DEF, BC) < 10"
  "div(BC, A) < 10"
  
  --answer="(A, BC, DEF, GHIJ)"
  

  Solution: The 4-digit number is 3402.

  We have:

  3402 = 6 × 567
  567 = 7 × 81
  81 = 9 × 9
  9

  And between them the numbers 9, 81, 567, 3402 use each of the digits 0-9 exactly once.

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  Ruud 2:21 pm on 2 January 2026 Permalink | Reply

  Here is recursive solution:

  import istr
  
  def expand(n="", used=[]):
      for d in range(1, 10):
          next_n = d * istr(n if n else 1)
          next_used = used + [next_n]
          if len(next_n) == len(n) + 1 and istr("").join(next_used).all_distinct():
              if len(next_n) == 4:
                  print(*next_used)
              else:
                  expand(n=next_n, used=next_used)
  
  expand()
  

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  GeoffR 4:54 pm on 2 January 2026 Permalink | Reply

  % A Solution in MiniZinc
  include "globals.mzn";
  
  var 1..9: a; var 0..9: b; var 0..9: c; var 0..9: d;
  var 1..9: e; var 0..9: f; var 0..9: g;
  var 1..9: h; var 0..9: i; var 1..9: j;
  
  constraint all_different ([a, b, c, d, e, f, g, h, i, j]);
  
  var 1000..9999: abcd == 1000*a + 100*b + 10*c + d;
  var 100..999: efg == 100*e + 10*f + g;
  var 10..99: hi == 10*h + i;
  var 2..9: d1; var 2..9: d2; var 2..9: d3; 
  
  % Four, three and two digut number constraints
  constraint abcd div efg == d1 /\ d1 * efg == abcd;
  constraint efg div hi == d2 /\ d2 * hi == efg;
  constraint hi div j == d3 /\ d3 * j == hi;
  
  solve satisfy;
  
  output ["The four-digit number was " ++ show(abcd)
  ++ "\n" ++ "[a, b, c, d, e, f, g, h, i, j] = "
  ++ "\n" ++ show([a, b, c, d, e, f, g, h, i, j]) ];
  
  % The four-digit number was 3402
  % [a, b, c, d, e, f, g, h, i, j] = 
  % [3, 4, 0, 2, 5, 6, 7, 8, 1, 9]
  % ----------
  % ==========
  
  
  

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