Measured Steps

Twenty-five ants are placed randomly on a meter stick. Each faces east or west. At a signal they all start to march at 1 centimeter per second. Whenever two ants collide they reverse directions. How long must we wait to be sure that all the ants have left the stick?

This sounds immensely complicated, but with a simple insight the answer is immediately clear. What is it?

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Spud Loops

Given any pair of potatoes — even bizarre, Richard Nixon-shaped potatoes — it’s always possible to draw a loop on each so that the two loops are identical in three dimensions.

Do you see the simple, intuitive proof for this?

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The Three Cards Problem

I show you three cards. One is white on both sides, one is black on both sides, and one is white on one side and black on the other. I shake them in a hat, remove one at random, and place it on a table. The side that’s face up is black. What’s the probability that the other side is also black?

Hint: It’s not 1/2.

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“Enigmatical Prophecies”

In his almanac, Ben Franklin made some alarming predictions for the year 1736: He said that the sea would rise and put New York and Boston under water, and that American vessels would be taken out of port “by a power with which we are not now at war.”

A year later he announced he’d been right: Seawater evaporates and descends as rain, and we are not at war with the wind.

The Apple Conundrum

Two women are selling apples. The first sells 30 apples at 2 for $1, earning $15. The second sells 30 apples at 3 for $1, earning $10. So between them they’ve sold 60 apples for $25.

The next day they set the same goal but work together. They sell 60 apples at 5 for $2, but they’re puzzled to find that they’ve made only $24.

What became of the other dollar?


Plutarch wrote that Homer died of exasperation because he couldn’t solve a fisherman’s riddle:

“What we have caught we threw away; what we could not catch we kept.”

The answer is “fleas.”

Setup Job


From Henry Ernest Dudeney, Amusements in Mathematics (1917):

I have a single chessboard and a single set of chessmen. In how many different ways may the men be correctly set up for the beginning of a game? I find that most people slip at a particular point in making the calculation.

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the puzzled fox

This 1872 Currier and Ives print is titled The Puzzled Fox: Find the Horse, Lamb, Wild Boar, Men’s and Women’s Faces. There are eight human and animal faces hidden in the scene. Can you find them?

Ironically, the birds that are visible have now disappeared — they’re passenger pigeons.