Fairy Tale Math Circle #9

In case you’re wondering, there was no Circle #8. Rocket Boy was sick, Rocket Dad was out of town and I had to cancel. But this Monday we were back in business with a new fairy tale, The Princess and the Pea.

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The first problem was to find all the paths from points A to point B if we can only follow black lines and make no more than three turns. The kids worked in pairs for this one. It was up to them to choose how to keep track of the solutions.

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Some chose to rely on memory. Is it the best strategy? How do we check if we already walked the same path?

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Little M, who joined us for this puzzle, came up with a wonderful idea of using different color markers for different paths. For a while he was the only one employing this strategy. So I asked if I could share his approach with the rest of the group.

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It worked! Here’s the team that did it all in their heads and kept coming up with wrong answers because they kept counting the same paths more than once. Once they adopted the different paths different colors strategy they quickly solved the problem.

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Next came a number puzzle. That one required some attention to detail since no digit in the puzzle could repeat. It was also the key to solving it.

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For a while I was getting lots of interesting solutions. None of them were correct. Now I’m thinking a bit more about how this puzzle is really similar in some ways to the first puzzle. Unless there are strict rules placed on them, both produce infinitely many solutions. Most everyone in the group started by trying different combinations, going through 5-8 iterations. Only S found the solution. The rest grew tired and restless.

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Time for a totally irresponsible experiment that combined princesses, peas and whoopie cushions. Why do they make such a funny noise? Ah, now everyone is paying attention!

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Can we create our own instruments that exploit the Bernoulli principle to make funny noises? What do they look and sound like? The ones we made with pipes and balloons sounds like elephants. Hmm, is that how elephant’s trunk work?

Next week we will not be starting a new fairy tale. Instead, we will be working on unsolved problems from the previous meetings.

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