S2T2

Jim Randell 9:10 am on 10 February 2022 Permalink Reply
Tags: by: Victor Bryant ( 139 )   

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  Jim Randell 9:11 am on 10 February 2022 Permalink | Reply

  If we suppose the three numbers are ab, cd, ef, and that 2 × ab = cd then we have:

  ab + cd + ef = ADD
  ab × cd × ef = TIMES

  And we can use the [[ SubstitutedExpression ]] solver from the enigma.py library to solve the alphametic expressions.

  The following run file executes in 59ms (the generated program has an internal runtime of 575µs).

  Run: [ @replit ]

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  --symbols="ADEIMSTabcdef"
  --distinct="ADEIMST,abcdef"
  --answer="(ab, cd, ef)"
  
  # cd is twice ab
  "2 * ab = cd"
  
  # sum is ADD, product is TIMES
  "ab + cd + ef = ADD"
  "ab * cd * ef = TIMES"
  
  # a, b, c, d, e, f are 6 consecutive digits
  --code="is_consecutive = lambda *vs: all(y == x + 1 for (x, y) in tuples(ordered(*vs), 2))"
  "is_consecutive({a}, {b}, {c}, {d}, {e}, {f})"
  
  # [optional]
  --template="(ab + cd + ef = ADD) (ab * cd * ef = TIMES)"
  --solution=""
  

  Solution: The three original numbers are: 23, 46, 75.

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  • 

    Frits 1:17 pm on 10 February 2022 Permalink | Reply

    Instead of the all(…) condition you can also use:

    "(s := sorted([{a}, {b}, {c}, {d}, {e}, {f}]))[-1] - s[0] == 5"
    

    or

    "max(s := [{a}, {b}, {c}, {d}, {e}, {f}]) - min(s) == 5"
    

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• 

  GeoffR 3:07 pm on 10 February 2022 Permalink | Reply

  Using Frits second suggestion proved useful in a MiniZinc solution.

  
  % A Solution in MiniZinc
  include "globals.mzn";
  
  % Digits forming three 2-digit numbers ab, cd, ef
  var 1..9:a; var 1..9:b; var 1..9:c; 
  var 1..9:d; var 1..9:e; var 1..9:f;
  
  constraint all_different([a, b, c, d, e, f]);
  
  % The three 2-digit numbers used six consecutive digits between them
  constraint max([a,b,c,d,e,f]) - min([a,b,c,d,e,f]) == 5;
  
  var 10..99:ab == 10*a + b;
  var 10..99:cd == 10*c + d;
  var 10..99:ef == 10*e + f;
  
  constraint cd == 2 * ab; 
  
  % Upper case letters
  var 1..9:A; var 0..9:D; var 1..9:T; var 1..9:I;
  var 0..9:M; var 0..9:E; var 0..9:S;
  constraint all_different([A, D, T, I, M, E, S]);
  
  % Upper case sum and multiplication values
  var 100..999:ADD = 100*A + 11*D;
  var 10000..99999:TIMES = 10000*T + 1000*I + 100*M + 10*E + S;
  
  constraint ab + cd + ef == ADD;
  constraint ab * cd * ef == TIMES;
  
  solve satisfy;
  output ["The three original numbers were " ++ show([ab, cd, ef]) ];
  
  % The three original numbers were [23, 46, 75]
  % ----------
  % ==========
  
  
  

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