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Puzzled: Solutions and Sources

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Dartmouth College Professor of Mathematics and of Computer Science Peter Winkler

Last month (February 2013) we posed a trio of brainteasers concerning probability and dice. Here, we offer solutions to all three. How did you do?

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Arnold Lebow

While 42 is the correct average time to get two sevens in a row is correct, the method used is incorrect.
That method would say that to get three sevens in a row takes average time 42*43; the correct answer is 6 + 6^2 + 6^3. The incorrect method give the correct answer since 6 + 6^2 = 6*7.

Phillip Burger

Re number 1. and the (6 choose 2) * (4 choose 2) * 1/2 component of the solution, (6 choose 2) and (4 choose 2) can both return the same pair resulting in N=3. Should this component actually be (6 choose 2) * (4 choose 2) * 1/2 - 6 instead, removing the six possible cases where (6 choose 2) * (4 choose 2) results in the same pair?

This problem is a bit of a stretch for me so my apologies upfront for not being able to better articulate my point of view.

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