023: Magic Hexagon

/*

  Magic hexagon in Picat.

  Prob023: Magic Hexagon
  http://www.comp.rgu.ac.uk/staff/ha/ZCSP/prob023/prob023.pdf
  http://www.cse.unsw.edu.au/~tw/csplib/prob/prob023/


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

*/

import cp.

main => go.

go =>

   LD = [A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S],
   LD :: 1..19,

   all_different(LD),

   A + B + C #=  38,
   D + E + F + G #=  38,
   H + I + J + K + L #=  38, 
   M + N + O + P #=  38, 
   Q + R + S #=  38, 
   A + D + H #=  38, 
   B + E + I + M #=  38, 
   C + F + J + N + Q #=  38, 
   G + K + O + R #=  38, 
   L + P + S #=  38, 
   C + G + L #=  38, 
   B + F + K + P #=  38, 
   A + E + J + O + S #=  38, 
   D + I + N + R #=  38, 
   H + M + Q #=  38, 
   
   A #< C,
   A #< H,
   A #< L,
   A #< Q,
   A #< S,
   C #< H,
   
   solve([ff], LD),

   writeln(LD),
   nl.