We consider the ways in which we might preserve a mattress. Every six months, as we all know, you should rotate or flip your mattress so that it wears out evenly. Is there a simple, easy to follow procedure for ensuring that the mattress cycles through all four possible orientations?

(This is really a lead-in for a discussion about Group Theory.)

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We catch Ed Pegg, puzzler extraordinaire , as he is going over a script for the TV show Numb3rs.

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We also asked, on this week’s segment how to label the faces of some ordinary dice, with twelve different numbers (we did say different didn’t we?) so that every roll produces a prime number. This puzzle is from the fascinating site www.primepuzzles.net. Don’t peek!

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A young listener (or really her father, on behalf of a young listener) wrote us:

Two players each choose any 10 digits from 1 to 36.

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(I have no idea why cakes are so popular in math puzzles, but here is another conundrum)

Peter Winkler gives us one more puzzle from his book Mathematical Mind Benders and tells us a little bit about why good puzzles are like good jokes.

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We’ve never discussed the famous “Monty Hall Problem” here (though we did talk about it on the radio before we started podcasting). We recently got an interesting letter that highlights the difference between a game like “Let’s Make A Deal” and a game like “Deal or No Deal”.

Mark A. recently wrote us:
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