## DX. Dumb Robots

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!

## DW. The Online Encyclopedia of Integer Sequences!

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!)

## DV. Dealing with Chaos

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

## DU. Chaos at the Card Table

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

## Follow Up: Smullyan’s 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.

## DT. Speaking of Self-reference

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

## DS. Math Chat With Frank Morgan

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!

## DR. Double Bubble

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

photo: Jeff Bauer

## DQ. We Are Not Liars

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.

## DP. Would Chuck Wood

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?