You have 15 pool balls arranged in a triangle.

What is the greatest number of balls you will ever have to swap in order to ensure that they are all in the correct position at the start of the game?

An allowable position is either the one in the diagram above, the same position mirrored left-to-right, or either of these arrangements with the red and yellow balls switched.

Just go rack up a rack of balls and see how many swaps it takes max... Stripes are red, solids are yellow, move the 8 out of place and mix it up as much as you can... i counted four moves... once you move the 8 ball into position you can only take a maximum of 3 more moves to move the rack into an allowable position... of course, this problem doesnt say anything about repeating moves, so i guess if you wanted to be nitpicky and contrary you could continuosly swithc the same to balls thereby creating an infinate number of maximum moves....

Posted by sean on 2005-08-16 21:07:49