Standard Podcast [ 15:50 ] Play Now | Play in Popup | Download

John. H. Conway, one of the young men pictured above, tells us about his fabulous and simple method for rapidly calculating the day of the week.

With just a little practice, you too can Impress your friends (or drive them away) with this stupendous ability!

Save Indiana, his girlfriend, his father and his father’s sidekick from certain doom! They must cross a bridge across a gorge in no more than one hour!
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Standard Podcast [ 11:22 ] Play Now | Play in Popup | Download

Niclas Hedell gives his solution to the third tree puzzle he posed last week, and we ask a puzzle about sums of numbers.

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Standard Podcast [ 10:17 ] Play Now | Play in Popup | Download

Niclas Hedell, a listener, poses a problem from his days in the Swedish military: given two trees in the forest, and a rope twice as long as the distance between the trees, how do you find a third tree so that all three make a right triangle.

And we explain how the Stork can catch the Frog.

Standard Podcast [ 8:36 ] Play Now | Play in Popup | Download

Amusingly, this problem has exactly the same solution as the proof that there are as many rational numbers as there are counting numbers. And the proof generalizes: one stork can catch three frogs, or ten or fifty.

Here are some bonus problems:

1. The stork can catch the frog even if it can start at any rational number and hop any fixed rational distance each step.
2. However, if the frog can start at any real number or hop any real distance, the stork has no strategy that guarantees a catch. This is, in effect, the same as proving that the real numbers are not countable.