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.

(In reply to Tedious work by Jonathan Chang)

Hi Jonathan,

I'm afraid you misunderstood the question.

"What is the greatest number of balls you will ever have to move" is a confusing sentence, but what it means is "assuming you always rearrange the balls in the LEAST number of moves, what is the MAXIMUM that this least number could be"?

If the balls started out in an arrangement such that two balls were out of place, the least number would be 1 (a single swap). Other arrangements would require more moves to get it to a starting position. What is the greatest number of moves you would ever be REQUIRED to make to get the balls to a correct starting position?

Edited on April 28, 2005, 3:13 pm

Posted by Sam on 2005-04-28 15:11:06