MATH STINGER #48
by Dr. Joel C. Fowler
Assistant Professor of Mathematics

The puzzle for this issue concerns thirty balls numbered 1 - 30 (like a double size set of pool balls) to be put away in a drawer one by one. The only restriction is that when a ball is placed in the drawer its number must be contiguous with those already in the drawer. For example, if the drawer currently contains balls numbered 3, 4, and 5 then the next ball to go in must be either number 2 or number 6. If the drawer currently contains balls numbered 26, 27, 28, 29, and 30 then the next ball to go in must be number 25 (since the numbers only go to thirty). The first ball to go in can be any number. The puzzle is to determine how many different ways the 30 balls can be put away subject to this restriction. That is, in how many different orders can the thirty balls be put away without ever placing a ball in the drawer whose number is isolated from the group of numbers already in the drawer?