/* 

  Pyramid missing number puzzle in Picat.

  From Muhammad Zain Sarwar: "People With an IQ of 140+ Can Find These Missing Numbers in This Pyramid!"
  """
          ?
        ?  56
      19  ?  28
     7  ?  ?_ ?
  _ ?  ?  7  ?  ? 
  """

       [103]
      [47,56]
     [19,28,28]
    [7,12,16,12]
    [2,5,7,9,3]



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

*/

import sat.

main => go.

go ?=>
  X = [      [_],
            [_,56],
          [19,_,28],
         [7,_,_,_],
       [_,_,7,_,_]],

  X :: 1..200,

  Ls = [  [[1,1],[2,1],[2,2]],
  
          [[2,1],[3,1],[3,2]],
          [[2,2],[3,2],[3,3]],
           
          [[3,1],[4,1],[4,2]],
          [[3,2],[4,2],[4,3]],
          [[3,3],[4,3],[4,4]],
            
          [[4,1],[5,1],[5,2]],
          [[4,2],[5,2],[5,3]],                      
          [[4,3],[5,3],[5,4]],
          [[4,4],[5,4],[5,5]]
        ],

  foreach(L in Ls)
    X1 = X[L[1,1],L[1,2]],
    X2 = X[L[2,1],L[2,2]],
    X3 = X[L[3,1],L[3,2]],
    X1 #= X2 + X3
  end,

  solve(X),
  
  println(X),
  foreach(Row in X)
    println(Row)
  end,
  nl,
  fail,
  
  nl.
go => true.
  

/*
  Are there some other solutions?
  Well, these are not very interesting...

[[104],[47,56],[19,27,28],[7,11,15,12],[3,3,7,7,4]]
[a = 1,b = 1,c = 1]
[104]
[47,56]
[19,27,28]
[7,11,15,12]
[3,3,7,7,4]

[[103],[47,56],[19,28,28],[7,12,16,12],[2,5,7,9,3]]
[a = 1,b = 1,c = 0]
[103]
[47,56]
[19,28,28]
[7,12,16,12]
[2,5,7,9,3]

[[105],[47,56],[19,26,28],[7,10,14,12],[4,1,7,5,5]]
[a = 1,b = 1,c = 2]
[105]
[47,56]
[19,26,28]
[7,10,14,12]
[4,1,7,5,5]

[[102],[47,56],[19,29,28],[7,13,17,12],[1,7,7,11,2]]
[a = 1,b = 1,c = -1]
[102]
[47,56]
[19,29,28]
[7,13,17,12]
[1,7,7,11,2]


*/
go2 ?=>
  nolog,
  X = [      [_],
            [_,56],
          [19,_,28],
         [7,_,_,_],
       [_,_,7,_,_]],

  X :: 1..10000,

  [A,B,C] :: -10..10,

  Ls = [  [[1,1],[2,1],[2,2]],
  
          [[2,1],[3,1],[3,2]],
          [[2,2],[3,2],[3,3]],
           
          [[3,1],[4,1],[4,2]],
          [[3,2],[4,2],[4,3]],
          [[3,3],[4,3],[4,4]],
            
          [[4,1],[5,1],[5,2]],
          [[4,2],[5,2],[5,3]],                      
          [[4,3],[5,3],[5,4]],
          [[4,4],[5,4],[5,5]]
        ],

  foreach(L in Ls)
    X1 = X[L[1,1],L[1,2]],
    X2 = X[L[2,1],L[2,2]],
    X3 = X[L[3,1],L[3,2]],
    X1 #= A* X2 + B* X3 + C
  end,

  Vars = X ++ [A,B,C],
  solve(Vars),
  
  println(X),
  println([a=A,b=B,c=C]),
  foreach(Row in X)
    println(Row)
  end,
  nl,
  fail,
  
  nl.
go2 => true.