S2T2

Jim Randell 8:06 am on 8 March 2019 Permalink Reply
Tags: by: Danny Roth ( 84 ), flawed ( 52 )   

• 

  Jim Randell 8:07 am on 8 March 2019 Permalink | Reply

  We can feed the alphametic expressions directly to the [[ SubstitutedExpression() ]] solver from the enigma.py library.

  This run-file executes in 125ms.

  Run: [ @replit ]

  #! python3 -m enigma -rr
  
  SubstitutedExpression
  
  --answer="ABCDEFGHIJ"
  
  "A + G = C"
  "B * J = FH"
  "GE * AI = HDB"
  

  Solution: There are two solutions: ABCDEFGHIJ = 1840253697, and ABCDEFGHIJ = 3840951627.

  The two solutions arise as we can swap the values of (A, E) with (G, I). One of them is (1, 2) and the other is (3, 9).

  Apparently the setter was unaware that there were two solutions, which seems a bit odd as this kind of puzzle can very easily be checked. For example my own alphametic solver is available here [ https://repl.it/@jim_r/alphametic ]. Click “Run”, enter the expressions, and you get the two solutions straight away. [Note: As of 2024 code sharing via replit no longer works].

  Here’s an example transcript:

  Python 3.6.1 (default, Dec 2015, 13:05:11)
  [GCC 4.8.2] on linux
  expr[0] (or enter) >>> A + G = C
  expr[1] (or enter) >>> B * J = FH
  expr[2] (or enter) >>> GE * AI = HDB
  expr[3] (or enter) >>>
  (A + G = C) (B * J = FH) (GE * AI = HDB)
  (1 + 3 = 4) (8 * 7 = 56) (32 * 19 = 608) / A=1 B=8 C=4 D=0 E=2 F=5 G=3 H=6 I=9 J=7
  (3 + 1 = 4) (8 * 7 = 56) (19 * 32 = 608) / A=3 B=8 C=4 D=0 E=9 F=5 G=1 H=6 I=2 J=7
  [2 solutions]
  [timing] elapsed time: 0.0016964s (1.70ms)
  

  ---

  The published solution is:

  Teaser 2938
  There were two possible correct answers: 1840253697 or 3840951627.
  We apologise for any confusion.

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• 

  GeoffR 1:20 pm on 8 March 2019 Permalink | Reply

  % A solution in MinZinc 
  include "globals.mzn";
  
  var 0..9: A; var 0..9: B; var 0..9: C; var 0..9: D; var 0..9: E;
  var 0..9: F; var 0..9: G; var 0..9: H; var 0..9: I; var 0..9: J;
  
  constraint A != 0 /\ G != 0 /\ C != 0 /\ B != 0 
  /\ J != 0 /\ F != 0 /\ H != 0;
  
  constraint all_different ( [A,B,C,D,E,F,G,H,I,J] );
  
  var 10..99: FH = 10*F + H;
  var 10..99: GE = 10*G + E;
  var 10..99: AI = 10*A + I;
  var 100..999: HDB = 100*H + 10*D + B;
  
  constraint A + G == C;
  constraint B * J == FH;
  constraint GE * AI = HDB;
  
  solve satisfy;
  
  output [ "ABCDEFGHIJ = " ++ show(A),show(B),show(C),show(D),show(E),
  show(F),show(G),show(H),show(I),show(J) ];
  
  % ABCDEFGHIJ = 3840951627
  % ABCDEFGHIJ = 1840253697
  
  

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