Petals Around the Rose: Fraternity Register

Learned this game at a Barn Players Summer Theater Christmas party in Miles City, MT, many, many years ago. There I was told that the only thing I could be told was that the name of the game was Polar Bears Around the Ice Hole, but that some people called the game Rose Petals Around the Rose. No mention was made of the number always being even, and, frankly, I prefer it that way.