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.

the problem says find greatest number of balls that have to be moved. The answer has to be 15, since you can't move more balls than the amount you have.

If this problem was meant to find out how many times a ball needed to be swapped(although the question didnt ask for this this), then the answer would be infinity, since you can continuously switch the same 2 balls.

Posted by Nik on 2005-04-29 03:40:37