Neurobics

Petals Around the Rose

Over the years particular puzzles, games, and problems have suddenly become immensely popular, fashionable even. Sam Lloyd's "15 Puzzle" invented in about 1880 is one that comes to mind. In it squares numbered one to fifteen are slid around inside a four-by-four square frame with the idea of arranging them in order. Other versions of this perennially popular puzzle require the composition of a picture from the fifteen scrambled squares.

More recent examples of fashionably popular puzzles and games are the word game "Netters" [NZSM,September 1992] and "Petals Around the Rose". In the latter, a person in the know, called a "Potentate of the Rose", invites someone to throw five dice. When this is done, the potentate responds with a number. The number is determined by the dots on the dice and the challenge is to work out how.

One piece of information is supplied -- that the name of the puzzle has something to do with how the numbers are obtained. One rule is also given -- that once you have solved the puzzle you also become a Potentate of the Rose and from then on may not divulge the solution to anyone else.

If you've not come across the puzzle before, give it a try, but beware, it can be an exasperating problem. I have known mathematicians to give up on it, but academically modest youngsters to solve it in less than five minutes -- and that may be a clue.

Above are the results of six throws of five dice, with the Potentate's numbers alongside. How were the numbers obtained? What number does the last row of dice determine?

Incidentally, all I've been able to discover concerning the origin of this puzzle is that it is "credited to Kurt A. Christoff who got it from George Martin". If any reader is able to fill in further details I'd be pleased to hear from them.

Russell Dear is a Mathematician living in Invercargill