May 13, 2008
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math puzzles, numbers, The Mathcast

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!

And we have a quick puzzle from Jeff Yoak, on crashing dumb robots together!

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May 5, 2008
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Favorites, guests, numbers, The Mathcast

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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May 5, 2008
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answers, logic, The Mathcast

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

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April 18, 2008
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Favorites, guests, math puzzles, The Mathcast

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

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April 17, 2008
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Follow Up, guests, paradoxes

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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April 9, 2008
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answers, guests, Mathfactor Events, The Mathcast, Topology and geometry

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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April 1, 2008
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Favorites, guests, The Mathcast, Topology and geometry

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

photo: Jeff Bauer

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March 26, 2008
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answers, guests, logic, math puzzles, Mathfactor Events, paradoxes, The Mathcast

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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March 19, 2008
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logic, math puzzles, The Mathcast

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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