Three hockey pucks, A, B, and C, lie in a plane. You make a move by hitting one puck so that it passes between the other two in a straight line. Is it possible to return all the pucks to their original positions with 1001 moves?
From Arthur Engel, ProblemSolving Strategies, 1998.
Consider the direction, clockwise or counterclockwise, in which the pucks define the vertices of a triangle. When one is shot through the line segment joining the other two, this is reversed. After an odd number of such shots, such as 1001, the chirality is reversed from the original, so No it's not possible to return them to their original positions with 1001 moves.

Posted by Charlie
on 20150825 14:31:58 