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 either extremely simple or impossible by Nik)

A lot of people now seem to be confused about this, but it really shouldn't be that complicated.

"...the greatest number that you ever have to swap in order to ensure that they are in the correct position."

You would never have to swap an infinite number of balls, nor two balls back and forth, to get them in the correct position.  However, if two balls were out of place, you would have to swap them.

Immagine you were looking at them all out of order. You might say "Oh drat! I have to swap six balls before they're all correct." You would never say "Oh drat! I have to swap an infinite number of balls before they're all correct."

So in which situation would you ever need to swap the most number of balls before you can get them back in their correct positions?

Posted by Sam on 2005-04-29 11:36:59