Recalling Yesterday

From P.M.H. Kendall and G.M. Thomas, Mathematical Puzzles for the Connoisseur, 1962:

I’ve just been reading Jules Verne’s Around the World in Eighty Days — you know, where Phileas Fogg lost a day on the way round. Our science master says that ships put it right nowadays by having a thing called a Universal Date Line in the Pacific. When you cross the line from East to West you put the calendar on a day; and when you cross it the other way you put the calendar back. What I want to know is, when Puck put a girdle round the Earth in forty minutes and presumably did the right thing on crossing the Date Line, why didn’t he get back on the day before he started — or the day after, according to which way round he went?

I asked the English master this and he got quite cross about it and said it was nothing to do with Shakespeare. But if you flew round the earth as quickly as Puck it would matter, wouldn’t it?

Wouldn’t it? Why doesn’t Puck lose a day?

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The Annual Liars

Two brothers are scrupulously truthful, with one exception: Each lies about his birthday on his birthday.

On New Year’s Eve you ask what their birthdays are. The first says “Yesterday” and the second says “Tomorrow.”

On New Year’s Day you ask again what their birthdays are. Again the first says “Yesterday” and the second says “Tomorrow.”

What are their birthdays?

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A Chess Maze

nelson chess maze

Harry L. Nelson offered this puzzle in the Journal of Recreational Mathematics in 1983. The black king’s favorite square is c8, but he finds it is under attack by a white pawn. In how few moves can he correct this problem and return to a peaceful c8? White never moves. The black king can capture white pieces, but he may not visit any square more than once and may not enter check.

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A Thought Experiment

Suppose you have two identical bolts. Hold each by its head, engage the threads as shown, and revolve one about the other. Will this action pull the heads closer together or drive them farther apart?

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A Pretty Problem

In Longfellow’s novel Kavanagh, Mr. Churchill reads a word problem to his wife:

“In a lake the bud of a water-lily was observed, one span above the water, and when moved by the gentle breeze, it sunk in the water at two cubits’ distance. Required the depth of the water.”

“That is charming, but must be very difficult,” she says. “I could not answer it.”

Is it? If a span is 9 inches and a cubit is 18 inches, how deep is the water?

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For 25 years, Macalester College mathematician Joe Konhauser offered a “problem of the week” to his students. Here’s a sample, from the collection Which Way Did the Bicycle Go? (1996):

Fifteen sheets of paper of various sizes and shapes lie on a desktop, covering it completely. The sheets may overlap one another and may even hang over the edge of the desktop. Prove that five of the sheets can be removed so that the remaining ten sheets cover at least two-thirds of the desktop.

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Even Steven

A Scholar traveyling, and having noe money, call’d at an Alehouse, and ask’d for a penny loafe, then gave his hostesse it againe, for a pot of ale; and having drunke it of, was going away. The woman demanded a penny of him. For what? saies he. Shee answers, for ye ale. Quoth hee, I gave you ye loafe for it. Then, said she, pay for ye loafe. Quoth hee, had you it not againe? which put ye woman to a non plus, that ye scholar went free away.

— John Ashton, Humour, Wit, & Satire of the Seventeenth Century, 1883