S2T2

Jim Randell 8:40 am on 10 November 2022 Permalink Reply
Tags: by: Danny Roth ( 84 )   

• 

  Jim Randell 8:40 am on 10 November 2022 Permalink | Reply

  We can use the [[ SubstitutedExpression.split_sum() ]] solver from the enigma.py library to solve this puzzle.

  The following run file executes in 58ms. (Internal runtime is 4.74ms).

  Run: [ @replit ]

  from enigma import (SubstitutedExpression, irange, diff, join, printf)
  
  # construct the alphametic sum
  p = SubstitutedExpression.split_sum(
    ["THIRTY"] * 2 + ["TEN"] * 4, "HUNDRED",
    template="(2 * {THIRTY} + 4 * {TEN} = {HUNDRED})",
  )
  
  # solve the puzzle, and output unused digit(s)
  for s in p.solve():
    ds = diff(irange(0, 9), s.values())
    # output solution
    printf("-> unused digits = {ds}", ds=join(ds, sep=", "))
  

  Solution: The missing digit is 7.

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• 

  GeoffR 11:40 am on 10 November 2022 Permalink | Reply

  
  % A Solution in MiniZinc
  include "globals.mzn";
  
  %          T H I R T Y
  %          T H I R T Y
  %                T E N
  %                T E N
  %                T E N
  %                T E N
  %        -------------
  %        H U N D R E D
  %        -------------
  
  set of int: INT = 0..9;
  var INT: T; var INT: H; var INT: I;
  var INT: R; var INT: Y; var INT: E;
  var INT: N; var INT: U; var INT: D;
  
  constraint T > 0 /\ H > 0;
  constraint all_different( [T,H,I,R,Y,E,N,U,D]);
  
  % Carry digits from RH end
  var 0..6:c1; var 0..6:c2; var 0..6:c3;
  var 0..1:c4; var 0..1:c5; var 0..1:c6;
  
  % Adding digits in columns, with carry digits from RH end of sum
  constraint D == (4*N + 2*Y) mod 10 /\ c1 == (4*N + 2*Y) div 10;
  constraint E == (c1 + 4*E + 2*T) mod 10 /\ c2 == (c1 + 4*E + 2*T) div 10;
  constraint R == (c2 + 4*T + 2*R) mod 10 /\ c3 == (c2 + 4*T + 2*R) div 10;
  constraint D == (c3 + 2*I) mod 10 /\ c4 == (c3 + 2*I) div 10;
  constraint N == (c4 + 2*H) mod 10 /\ c5 == (c4 + 2*H) div 10;
  constraint U == (c5 + 2*T) mod 10 /\ c6 == (c5 + 2*T) div 10;
  constraint H == c6;
  
  solve satisfy;
  
  output ["[T,H,I,R,Y,E,N,U,D] = " ++ show([T,H,I,R,Y,E,N,U,D]) ];
  % [T, H, I, R, Y, E, N, U, D] = 
  % [9, 1, 5, 2, 6, 0, 3, 8, 4]
  % ----------
  % ==========
  % By inspection, missing digit = 7.
  % TEN = 903, THIRTY = 915296, HUNDRED = 1834204.
  
  

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• 

  GeoffR 10:25 pm on 10 November 2022 Permalink | Reply

  
  % A Solution in MiniZinc
  include "globals.mzn";
   
  %          T H I R T Y
  %          T H I R T Y
  %                T E N
  %                T E N
  %                T E N
  %                T E N
  %        -------------
  %        H U N D R E D
  %        -------------
   
  set of int: INT = 0..9;
  var INT: T; var INT: H; var INT: I;
  var INT: R; var INT: Y; var INT: E;
  var INT: N; var INT: U; var INT: D;
   
  constraint T > 0 /\ H > 0;
  constraint all_different( [T,H,I,R,Y,E,N,U,D]);
   
  var 100..999:TEN = 100*T + 10*E + N;
  var 100000..999999:THIRTY = 100000*T + 10000*H + 1000*I + 100*R + 10*T + Y;
  var 1000000..9999999:HUNDRED = 1000000*H + 100000*U + 10000*N + 1000*D + 100*R + 10*E + D;
  
  constraint 2 * THIRTY + 4 * TEN == HUNDRED;
  
  solve satisfy;
  
  output [ "T,H,I,R,Y,E,N,U,D] = " ++ show( [T,H,I,R,Y,E,N,U,D] ) ];
  
  % [T, H, I, R, Y, E, N ,U, D] = 
  % [9, 1, 5, 2, 6, 0, 3, 8, 4]
  % time elapsed: 0.17 s
  % ----------
  % ==========
  % By inspection, the missing digit is 7.
  
  
  

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