GeekDad Puzzle of the Week – Bayesian Orthodontics

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Just look at that guy… somehow, him loosing a tooth (loosing, not losing — he knew where it was the entire time!) made him even more adorable. I believe that he is still the first one in his class to loose a tooth, but that may have already changed. So much happens so fast with little people his age!

maxtooth

This week’s puzzle centers around teeth, and probability and patterns of loosing teeth. At some point, Max will have loosed his first three (3) teeth. Based upon the standard starting number of teeth in the mouth of someone his age, there are only so many ways that he could loose them. If the pattern by which teeth are loosed is truly random, we can calculate the odds of any given student in his class having loosed the same three teeth as their first loosed, but not necessarily in the same order.

What is the minimum number of students that would need to be in his class for there to be a 50/50 chance of another student loosing their first three teeth in the same positions? A correct answer nets you a chance in the drawing for this week’s $50 ThinkGeek Gift Certificate.

NOTE: If this type of puzzle looks familiar, it should. There is a similar classic puzzle around natal anniversaries.

As always, please send your entries in to GeekDad Central for a chance at the drawing. Good luck, and happy puzzling!

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