/* 

  Enigma 1671 in Picat.

  https://enigmaticcode.wordpress.com/2011/11/30/enigma-1671-power-engineering/
  From New Scientist #2837, 2nd November 2011
  Read from left to right, the different digits in the number ENIGMA are 
  in descending order, and not necessarily consecutive.
  Given that E^6 + NI^3 + GMA^2 = EENNGG, find ENIGMA.

% Jim Randall's solution: Solution: ENIGMA = 876432.


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

*/


% import util.
import cp.


main => go.


go =>

  X = [E,N,I,G,M,A],
  X :: 1..9,

  all_different(X),
  decreasing(X),
  E**6 + (N*10+I)**3 + (G*100+M*10+A)**2 #= E*100000 + E*10000 + N*1000 + N*100 + G*10 + G,
  solve([ff,split], X),

  println(X),
  
  nl.