Solving Queens using J and brute force all permutations.

   randomboard =: 3 : '? (y,y) $ y'
   testsolution =: 4 : 0          NB. solution is a list of columns.
   m =. x
   n =. #x
   solution =. y A. i. n
   regions =.  ({&m) <"1 (i. n) ,. solution
   distinctregions =. n -: # ~. regions
   adjacentregions =. 1 e. |2-/\solution
   distinctregions *  -. adjacentregions
   )
   findsolution =:3 : 0
   board =: y
   ns =. 1 i.~ (board & testsolution)"0 i. !#y
   if. (ns = !#y) do. 'No solution found' 
   else.
 echo 'Solution index is ', ": ns
 ns A. i. #y end.
   )
   
   regions =: 4 : 0
   ({&x) <"1 (i. #x) ,. y
   )
   number2solution =: 4 : 0
   y A. i. #x
   )

   writesolution =: 4 : 0
   board =. x
   sol =.y
   m1 =. m
   n1 =. #x
   count =. 0
   for_a. sol do.
     m1 =. n1 (< count , a) } m1
     count =. count + 1
   end.
   m1
   )
   
   writewithsolution=: 4 : 0
   m1 =: x writesolution y
   (":"1 x) ,. '|' ,. ":"1 m1
   )
   
   m =: randomboard 9
   echo m writewithsolution findsolution m