The Hockey Puck Puzzle Page

• you may flip over any half of the disk bounded by a cut, leaving the other half unmoved (of course this will change the colors of those pie slices which were flipped);
• you may rotate the disk by any multiple of 30^o.

Hockey Puck Puzzle

Basic moves: For the i^th radial segment, let f_i be the transformation which flips over that half of the circle which contains the i^th pie piece. Let r denote the rotation of this circle by 30^o radians counterclockwise, so r=(1,2,...,12).

Solution strategy:

• Step 1: Solve half of the puzzle by "fishing", using moves of the form f_n*r^-1*f_n*r, where n is choosen appropriately.
• Use moves of the form (f₁*f₂*f₃*f₄* f₅*f₆)² to swap adjacent puzzle pieces (in this case, this move swaps 1 with 12 and flips over evry piece).