That the worm falls off the end of the rope depends on the fact that the incredible
harmonic series

1 + 1/2 + 1/3 + 1/4 + . . .
diverges to infinity, growing as large as you please!

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Dana Richards, editor of Martin Gardner’s Colossal Book of Short Puzzles and Problems explains why the worm makes it, in only about 15,092,688,622,113,788,323,693,563,264,538,101,449,859,497 steps! (Give or take a few.) This incredible fact depends on the mysterious Harmonic Series, discussed a little more in our next post.

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Dana Richards, editor of The Colossal Book of Short Puzzles and Problems discusses the amazing Martin Gardner and his legacy!

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Mathemagician Art Benjamin explains some of the tricks of his trade!

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Art Benjamin, mathemagician at Harvey Mudd, staggers, astounds and entertains!

Eric Demaine of MIT will control your minds across all time and all space!

Not surprisingly, we suppose, this trick is closely related to an important mathematical tool of the telecommunications industry:

Gray Codes are tremendously useful; a great, very readable discussion is in Chapter 2 of Martin Gardner’s Knotted Donuts and Other Mathematical Entertainments.

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The Collatz function on the counting numbers is really quite amazing: Divide by 2 if you can, otherwise multiply by 3 and add 1. Iterating this seems always to lead to the loop … 4, 2, 1, 4, 2, 1

For example: 7 → 22 → 11 → 34 → 17 → 52 → 26 → 13 → 40 → 20 → 10 → 5 → 16 → 8 → 4 → 2 → 1 → 4 → 2 → etc.

Does this always happen??

Dunno. No one does. But it is known that you will eventually loop if you start with any number up to about 5 x 10^19

(we accidentally exaggerated this in the podcast).

Try it for 27 for a daunting peek at the difficulty of this problem!

We explore Barry Cipra’s Tag Deal a bit more…

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Mathematics writer Barry Cipra shows us Tag Deal, a simple but perplexing puzzle with cards.

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We catch up with Raymond Smullyan, author of many fantastic books on logic, puzzles and paradoxes at this year’s Gathering for Gardner!

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