4⁵ + 1⁵ + 5⁵ + 0⁵ = 4150

In the desert, a bandit shoots a sheriff. The wounded sheriff rides into town, where the outraged townspeople form a mob. They track the bandit to his desert hideout and hang him. The sheriff dies a few days later.

Now: Did the bandit kill the sheriff? If so … when and where?

Solar eclipse, Aug. 11, 1999, seen from the Mir space station.

An eclipse appears total only while you’re directly in the moon’s shadow. Normally the darkness lasts only a few minutes … but in 1973 a Concorde supersonic jet managed to stay in the shade for 74 minutes.

The Arecibo Observatory is the largest single-aperture telescope ever built.

Astronomer Frank Drake calculated the dish would hold 357 million boxes of corn flakes.

Suppose some numbers are uninteresting. Put them in a separate class.

But now that class contains a largest and a smallest number. That’s interesting, so move them back into the class of interesting numbers.

You can repeat this until only one or two uninteresting numbers remain — a fact that makes them interesting. So now that class is empty, and all numbers are interesting.

In 1938, Stefan Banach proved that it’s always possible to slice a ham and cheese sandwich in half such that each half contains the same amount of bread, cheese, and ham.

It’s called the ham sandwich theorem.

27 × 81 = 2187
35 × 41 = 1435

Imagine a lottery with 1,000 tickets.

It’s rational to believe that one ticket will win.

But it’s also rational to believe that the first ticket will not win—nor the second, nor the third, and so on.

And isn’t that equivalent to believing that no ticket will win?