S2T2

Jim Randell 7:48 am on 28 March 2019 Permalink Reply
Tags: by: D Poulter ( 4 )   

• 

  Jim Randell 7:49 am on 28 March 2019 Permalink | Reply

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

  This run-file executes in 82ms.

  #! python -m enigma -rr
  
  SubstitutedExpression
  
  --digits="1-9"
  --answer="(ABC, DEF, GHI)"
  
  # the three 3-digit primes
  "is_prime(ABC)"
  "is_prime(DEF)"
  "is_prime(GHI)"
  
  # their sum is also a 3-digit number
  "ABC + DEF + GHI < 1000"
  
  # put them in order
  "ABC < DEF < GHI"
  

  Solution: The registration numbers are: 149, 263, 587.

  So, the setters registration number is 999.

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• 

  GeoffR 4:00 pm on 28 March 2019 Permalink | Reply

  % A Solution in MiniZinc
  include "globals.mzn";
  
  enum letters = {A, B, C, D, E, F, G, H, I};   
  array [letters] of var 1..9: v;
  
  constraint all_different (v);
  
  predicate is_prime(var int: x) = 
  x > 1 /\ forall(i in 2..1 + ceil(sqrt(int2float(ub(x))))) ((i < x) -> (x mod i > 0));
  
  var 100..999: ABC = 100*v[A] + 10*v[B] + v[C];
  var 100..999: DEF = 100*v[D] + 10*v[E] + v[F];
  var 100..999: GHI = 100*v[G] + 10*v[H] + v[I];
  var 100..999: XYZ;    % my car registration number
  
  constraint ABC + DEF + GHI == XYZ /\ GHI > DEF /\ DEF > ABC;
  
  constraint is_prime(ABC) /\ is_prime(DEF) /\ is_prime(GHI);
  
  solve satisfy;
  
  output[ "The three registration numbers of the visitors’ cars were " ++ show(ABC) 
  ++ ", " ++ show(DEF) ++ " and " ++ show(GHI) ]; 
  
  % The three registration numbers of the visitors’ cars were 149, 263 and 587
  
  
  

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