/* 

  The Digital Atom Smasher (alphametic problem) in Picat.

  From http://www.math.uni-bielefeld.de/~sillke/PUZZLES/ALPHAMETIC/
  """
  sqrt(ATOM)  =  A + TO + M
  
  this has two solutions
  Ref: Angela Fox Dunn, Mathematical Bafflers, 1980, p39 
  """


  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/

import cp.

main => go.


go ?=>

  X = [A,T,O,M],
  X :: 0..9,
  ATOM #= 1000*A+100*T+10*O+M,
  TO #= 10*T+O,

  Z :: 0..1000,
  Z * Z #= ATOM,

  all_different(X),
  Z #= A + (10*T+O) + M,

  solve(X ++ [Z]),
  println(X),

  println("ATOM = A + TO + M:"),
  printf("%w = %w + %w + %w\n",ATOM,A,TO,M),
  nl,
  fail,  
  nl.

go => true.