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?

Click for Answer

Paperwork

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.

Click for Answer

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

Trial by Fire

You are grilling steaks for Genghis Khan. Your little grill can broil two steaks at a time, but Genghis is hungry and wants three. That’s a problem: It takes 4 minutes to grill each side of a steak, so you’ll spend 8 minutes grilling the first two steaks, then another 8 grilling the third. Sixteen minutes is a long time to keep a warlord waiting.

How can you improve your time while still cooking the steaks thoroughly? Genghis really likes his well done.

Click for Answer

Do-Si-Do

do-si-do 4 x 3 chess puzzle

I’m not sure who originated this puzzle. Can the white queen force the black king onto square a1 of this 4 x 3 chessboard?

Click for Answer

Round and Round

http://commons.wikimedia.org/wiki/File:Donaueschingen_wappen.svg

Does the top of a rolling wheel move faster than the bottom? In his Cyclopedia of Puzzles (1914), Sam Loyd calls this “an old problem which has created a considerable discussion in the mechanical world.”

The rolling wheel retains its shape; it will arrive at its destination as a connected unit. This seems to imply that all of its parts are moving at the same speed. Yet the point in contact with the ground is moving not at all, while the top continuously overtakes it. Surely, then, the top is moving faster? “There is just enough of the mathematical and mechanical element in the make-up of the problem,” writes Loyd, “to provoke discussions from such as are well-up on these subjects.”

His answer: “The top of a wheel progresses exactly as fast as the bottom.” And, being Sam Loyd, he adds a wrinkle: “If the question referred to a mark on the tire the answer would be different, for the top is the highest point of the wheel and cannot revolve, for if it revolves the hundredth part of an inch it ceases to be the top.”

A second vexed wheel riddle; William James and Lewis Carroll consider related questions; a train moves simultaneously east and west.

Meant to Be

In 2007 Gordon Bonnet was going through some genealogical records when he ran across a marriage record for Edward DeVere Stewart and Etta Grace Staggers.

“It was only when I was putting the names in my database that I noticed something odd about them. What is it?”

Click for Answer

Huddled

http://books.google.com/books?id=J05AAAAAYAAJ&printsec=frontcover#v=onepage&q&f=false

By Sam Loyd. White to move and mate in two.

Click for Answer

Long Range

A puzzler from Willis Ernest Johnson, Mathematical Geography, 1907:

“A man was forty rods due east of a bear, his gun would carry only thirty rods, yet with no change of position he shot and killed the bear. Where on earth were they?”

Click for Answer