/** Solver for the Drive Ya Nuts puzzle:

   http://www.samstoybox.com/toys/DriveYaNuts.html

   solution:

   http://www.hasbro.com/common/instruct/DriveYaNuts.PDF   
*/

nuts = [[1,2,3,4,5,6],
        [1,4,3,6,5,2],
        [1,4,6,2,3,5],
        [1,6,2,4,5,3],
        [1,6,4,2,5,3],
        [1,6,5,3,2,4],
        [1,6,5,4,3,2]]

/** Now make a new array of dictionaries which map from
    (number on nut) to (position on nut) where (position on nut) is 0-based. */
nutPositions = new array
for nut=nuts
{
   nutPos = new dict
   
   for i=0 to 5
      nutPos@(nut@i) = i

   nutPositions.push[nutPos]
}

nutNums = array[0 to 6]
for pos = nutNums.permute[]
{
   nut0index = pos@0

   nut0pos0 = nuts@nut0index@0
   nut1index = pos@1
   nut1rotation = (3 - nutPositions@nut1index@nut0pos0) mod 6

   nut2index = pos@2
   nut0pos1 = nuts@nut0index@1
   nut2rotation = (4 - nutPositions@nut2index@nut0pos1) mod 6
   nut1pos2 = nuts@nut1index@((2 - nut1rotation) mod 6)
   nut2pos5 = nuts@nut2index@((5 - nut2rotation) mod 6)
   if (nut1pos2 != nut2pos5)
      next

   nut3index = pos@3
   nut0pos2 = nuts@nut0index@2
   nut3rotation = (5 - nutPositions@nut3index@nut0pos2) mod 6
   nut2pos3 = nuts@nut2index@((3 - nut2rotation) mod 6)
   nut3pos0 = nuts@nut3index@((0 - nut3rotation) mod 6)
   if (nut2pos3 != nut3pos0)
      next
   
   nut4index = pos@4
   nut0pos3 = nuts@nut0index@3
   nut4rotation = (0 - nutPositions@nut4index@nut0pos3) mod 6
   nut3pos4 = nuts@nut3index@((4 - nut3rotation) mod 6)
   nut4pos1 = nuts@nut4index@((1 - nut4rotation) mod 6)
   if (nut3pos4 != nut4pos1)
      next
   
   nut5index = pos@5
   nut0pos4 = nuts@nut0index@4
   nut5rotation = (1 - nutPositions@nut5index@nut0pos4) mod 6
   nut4pos5 = nuts@nut4index@((5 - nut4rotation) mod 6)
   nut5pos2 = nuts@nut5index@((2 - nut5rotation) mod 6)
   if (nut4pos5 != nut5pos2)
      next
   
   nut6index = pos@6
   nut0pos5 = nuts@nut0index@5
   nut6rotation = (2 - nutPositions@nut6index@nut0pos5) mod 6
   nut5pos0 = nuts@nut5index@((0 - nut5rotation) mod 6)
   nut6pos3 = nuts@nut6index@((3 - nut6rotation) mod 6)
   if (nut5pos0 != nut6pos3)
      next
   
   nut6index = pos@6
   nut6pos1 = nuts@nut6index@((1 - nut6rotation) mod 6)
   nut1pos4 = nuts@nut1index@((4 - nut1rotation) mod 6)
   if (nut6pos1 != nut1pos4)
      next
   
   println["Matching:  $pos"]

   println["Nut $nut0index " + nuts@nut0index + " is at the center,"]
   println[" with digit $nut0pos0 at its top."]

   println["Clockwise from top are nuts:"]
   for i=1 to 6
      println["   " + pos@i + " " + nuts@(pos@i)]
}