Standard Podcast [ 9:21 ] Play Now | Play in Popup | Download

We answer last weeks puzzle, discuss the law of small numbers and ask again what is the smallest positive counting number that Google can’t find?

Read the rest of this entry »

Standard Podcast [ 5:28 ] Play Now | Play in Popup | Download

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.

Standard Podcast [ 6:10 ] Play Now | Play in Popup | Download

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

Standard Podcast [ 9:15 ] Play Now | Play in Popup | Download

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

Standard Podcast [ 6:49 ] Play Now | Play in Popup | Download

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

Standard Podcast [ 8:37 ] Play Now | Play in Popup | Download

Faster than an exponential! More powerful than double factorials!! The Busy Beaver Function tops anything that could ever be computed– and we mean ever

Standard Podcast [ 16:25 ] Play Now | Play in Popup | Download

Those dumb robots can do anything! Anything at all, that any computer can do.

Standard Podcast [ 9:19 ] Play Now | Play in Popup | Download

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!)

Standard Podcast [ 14:16 ] Play Now | Play in Popup | Download

Standard Podcast [ 7:45 ] Play Now | Play in Popup | Download

In which we conclude our conversation and thwart the wicked King.