Pascal's triangle/Puzzle

Pascal's triangle/Puzzle is a programming puzzle. It lays out a problem which Rosetta Code users are encouraged to solve, using languages and techniques they know. Multiple approaches are not discouraged, so long as the puzzle guidelines are followed. For other Puzzles, see Category:Puzzles.

Here is a puzzle of Pyramid of numbers.

           [ 151]
          [  ][  ]
        [40][  ][  ]
      [  ][  ][  ][  ]
    [ X][11][ Y][ 4][ Z]

Each brick of the pyramid is the sum of the two bricks situated below this brick.
For the three missing numbers at the base of the pyramid : the one of the middle is the sum of the two other (that is, Y = X + Z).

Task:

• Find a solution of this puzzle.

Oz <ocaml>%% to compile : ozc -x <file.oz> functor

import

 System Application FD Search

define

 proc{Quest Root Rules}

   proc{Limit Rc Ls}
     case Ls of nil then skip
     [] X|Xs then
       {Limit Rc Xs}
       case X of N#V then        
         Rc.N =: V
       [] N1#N2#N3 then
         Rc.N1 =: Rc.N2 + Rc.N3
       end
     end
   end

   proc {Pyramid R}  
     {FD.tuple solution 15 0#FD.sup R}  %% non-negative integers domain
 %%          01      , pyramid format
 %%        02  03
 %%      04  05  06
 %%    07  08  09  10
 %%  11  12  13  14  15    
     R.1 =: R.2 + R.3     %% constraints of Pyramid of numbers
     R.2 =: R.4 + R.5
     R.3 =: R.5 + R.6
     R.4 =: R.7 + R.8
     R.5 =: R.8 + R.9
     R.6 =: R.9 + R.10
     R.7 =: R.11 + R.12
     R.8 =: R.12 + R.13
     R.9 =: R.13 + R.14
     R.10 =: R.14 + R.15
     
     {Limit R Rules}      %% additional constraints
     
     {FD.distribute ff R}   
   end
 in
   {Search.base.one Pyramid Root} %% search for solution   
 end

 local 
   Root R    
 in
   {Quest Root [1#151 4#40 12#11 14#4 13#11#15]} %% supply additional constraint rules
   if {Length Root} >= 1 then
     R = Root.1
     {For 1 15 1 
       proc{$ I} 
         if {Member I [1 3 6 10]} then
           {System.printInfo R.I#'\n'} 
         else
           {System.printInfo R.I#' '}  
         end     
       end
     }
   else
     {System.showInfo 'No solution found.'}
   end
 end

 {Application.exit 0}

end</ocaml>