25 February 2005

Petals Around the Rose

Found this interesting mathematical puzzle while reading other stuff online:

Petals Around the Rose. Warning: it can be very addictive.

Evidently some people -- math professors included -- take months or years to figure this puzzle out. Me? Truthfully, I tried it for about 10 minutes yesterday, then the answer came to me after some thought later that evening. I tried my solution out today, and I was right. I'd like to say it came to me "in a flash of insight", but really the solution didn't. It simply came to me after I considered the evidence that had been shown me, then visualized the puzzle in my head, and narrowed the solution set down based on the puzzle as visualized. Once the solution set was sufficiently narrow, iterating through the possibe solutions led easily to the realization of which solution was correct. Going back the web site to re-try the puzzle was just a verification step.

If you do figure it out, you can join the Fraternity of the Petals Around the Rose. Bill Gates is a member.

...Bill Gates hung on grimly.

Funny thing about Bill, he began to get answers right, but not consistently. He admitted that he was remembering throws he'd seen before, along with the answers, but had no plausible theory to account for answers. Remembering?

"Oh, sure," said the rememberer. "Like this throw...The answer is six... it's just like a roll we saw earlier..., except that the six this time was a two last time. I don't know why the answer is the same, but it is." The rotten kid must have had two dozen rolls, with answers, committed to memory by the time this discussion came up....

"I think I'd better use a piece of paper," said Bill, who was by this time the only active player who had still failed to divine the secret. "Aha," said he after about an hour and a half of this foolishness. "The answer is four on this roll."..."Yes."..."And the answer to this is ten."

He was right again, and he rattled off the next dozen answers without a quiver, declaring that he wasn't just remembering history now but knew what was going on. Like the others he didn't feel cheated by the game, but was satisfied that his effort paid off.

Some people who solved the puzzle quickly have expressed indignation about how quickly they solved it, and how this supposedly reflects badly on their intelligence. This is in response to one professor had commented that "The smarter you are, the longer it will take you to solve it" which personally I think is not only true, but is a useful clue to boot!

To them I say: The beauty of the puzzle needs to be found in the puzzle itself, and not in how intelligent other people will think you are if you do or don't solve it!