The Math Factor Podcast

 

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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!

Neil Sloane of ATT Labs shares some his favorite integer sequences from his online encyclopedia!

Recaman’s Sequence is especially perplexing! Sloane asks: does every number eventually appear?

(No one yet knows the answer!)

 

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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 present a recording of Raymond Smullyan’s lecture at the Gathering for Gardner, March 30, 2008; Newcomb’s paradox really is a stumper.

 

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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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Frank Morgan chats about math and gives us the solution to his bubble puzzle. If you’re in the area, don’t miss his lecture, Thursday April 10, at 7:30 pm in POSC 211!

 

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Frank Morgan of Williams College asks “What is the shape of a double bubble?”

 

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photo: Jeff Bauer

We discuss, among other things, whether all mathematicians are liars.

Send us your favorite paradoxes of this kind and we’ll report back on April 15.

 

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We consider that perennial spring conundrum: Would a woodchuck chuck her own wood if she would chuck wood for exactly those woodchucks who would not chuck their own wood?

 

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