Puzzles

Well Traveled

In Lord Dunsany’s Fourth Book of Jorkens, a member of the Billiards Club observes a book called On the Other Side of the Sun and says, “On the other side of the sun. I wonder what’s there.”

Jorkens, to everyone’s surprise, says, “I have been there.”

Terbut challenges this, but Jorkens insists he was on the other side of the sun six months ago. Terbut knows perfectly well that Jorkens was at the club six months ago, so he wagers £5 that Jorkens is wrong. Jorkens accepts.

“You have witnesses, I suppose,” says Terbut.

“Oh, yes,” says Jorkens.

“My first witness will be the hall-porter,” says Terbut. “And yours?”

“I am only calling one witness,” says Jorkens.

“Went with you to the other side of the sun?” asks Terbut.

“Oh, yes,” says Jorkens. “Six months ago.”

“And who is he?” asks Terbut.

Whom did Jorkens call?

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Black and White

shinkman chess problem

By William Anthony Shinkman. White to mate in two moves.

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Alcohol Problem

http://commons.wikimedia.org/wiki/File:Friedrich_Wahle_Der_Weinkenner.jpg

A bottle of fine wine normally improves with age for a while, but then goes bad. Consider, however, a bottle of EverBetter Wine, which continues to get better forever. When should we drink it?

— John L. Pollock, “How Do You Maximize Expectation Value?”, Noûs, September 1983

See The Devil’s Game.

Out of Sight

Several spherical planets of equal size are floating in space. The surface of each planet includes a region that is invisible from the other planets. Prove that the sum of these regions is equal to the surface area of one planet.

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Bad Behavior

You and I drive from Los Angeles to Las Vegas in separate cars. We depart simultaneously, and you stay always ahead of me, dutifully driving the speed limit throughout the trip. Nonetheless I get ticketed for speeding. How?

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Black and White

deutsche schachzeitung chess problem

From Deutsche Schachzeitung, 1890. White to mate in two moves.

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Animal Behavior

Martian snakes are elastic. If you take the tail of a Martian snake, and I take the head, and we pull in opposite directions, will there always be a part of the snake that doesn’t move?

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Reverses

A Hungarian problem shortlisted for the 30th International Mathematical Olympiad, 1989:

Around a circular race track are n race cars, each at a different location. At a signal, each car chooses a direction and begins to drive at a constant speed that will take it around the course in 1 hour. When two cars meet, both reverse direction without loss of speed. Show that at some future moment all the cars will be at their original positions.

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Black and White

markx chess problem

By B.J.M. Markx, 1897. White to mate in two moves.

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Weather Report

A puzzle contributed by Howard C. Saar to Recreational Mathematics Magazine, October 1962:

On the day before yesterday, the weatherman said, “Today’s weather is different from yesterday’s. If the weather is the same tomorrow as it was yesterday, the day after tomorrow will have the same weather as the day before yesterday. But if the weather is the same tomorrow as it is today, the day after tomorrow will have the same weather as yesterday.”

It is raining today, and it rained on the day before yesterday. What was the weather like yesterday? (Note: The prediction was correct!)

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Coverup

coverup puzzle diagram

Two squares have been removed from this 8×7 rectangle. Can the remaining 54 squares be tiled orthogonally with 18 3×1 tiles?

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Black and White

mccombe chess problem

By Alexander George McCombe. White to mate in two moves.

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Blocked

You have n cubical building blocks. You try to arrange them into the largest possible solid cube, but you find that don’t have quite enough blocks: One side of the large cube has exactly one row too few.

Prove that n is divisible by 6.

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Black and White

charlick chess problem

By Arthur Charlick. White to mate in two moves.

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Going Up

A problem from the 2003 Moscow Mathematical Olympiad:

A store has three floors, which are connected only by an elevator. At night the store is empty, and during the workday:

(1) Of the customers who enter the elevator on the second floor, half go to the first floor and half to the third floor.

(2) The number of customers who get out the elevator on the third floor is less than 1/3 the total number of customers who get out of the elevator.

Which is greater, the number of customers who go from the first floor to the second on a given workday, or the number who go from the first floor to the third?

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Too Late?

Paul R. McClenon of Washington D.C. contributed this problem to the January-February 1964 issue of Recreational Mathematics Magazine:

The poor patient read the prescription which would save his life. ‘Mix carefully a one-pint drink, made of scotch whisky and water, mixed one to five (1/6 scotch, 5/6 water). Drink it quickly and go to bed.’

However, the patient finds only the following items at hand:

A one-quart bottle, about half full of scotch whisky.
An eight-ounce glass.
An unlimited supply of water from his faucet.
A sink with a drain.
No other containers or measuring devices.

He can pour from either container to the other, without spilling a drop, and can fill either to the brim without loss. How should he mix the prescription? Will he figure it out in time? Will he be saved? Did a doctor or bartender write this prescription?

The magazine went out of business before it could publish the solution. I’ll leave it to you.

05/17/2013 UPDATE: There seem to be a number of ways to accomplish this. Here’s one:

We need a 16-ounce dose that’s 1/6 whiskey, so the final mixture must contain 2.666 ounces of whiskey.

  1. Fill the 8-ounce glass with whiskey, then empty the jug.
  2. Return the glassful of whiskey to the empty jug and add two glassfuls of water.
  3. Fill the glass with this 2-to-1 mixture of water and whiskey. The 8-ounce glass now contains 2.666 ounces of whiskey, our target.
  4. Empty the bottle, pour the glass’ contents into it, and add one 8-ounce glassful of water.

That leaves us with 16 ounces in the jug, 1/6 of which is whiskey and the rest water, as directed.

Thanks to everyone who wrote in.

Black and White

ramsey chess problem

By Robert Henry Ramsey. White to mate in two moves.

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“Illustrated Rebus”

http://books.google.com/books?id=jyQjAQAAMAAJ

From The Youth’s Companion, Sept. 25, 1879:

Why is this man likely to succeed in life?
Why do we know he has reached middle life?
How does the picture indicate his occupation?

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Black and White

shinkman chess problem

By William Anthony Shinkman. White to mate in two moves.

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Quick!

If you choose an answer to this question at random, what’s the chance that you’ll be correct?

(a) 25% (b) 50% (c) 0% (d) 25%

Black and White

campbell chess problem

By Joseph Graham Campbell. White to mate in two moves.

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Name Sense

A 1936 poser by British puzzle maven Hubert Phillips:

A man I met in Fleet Street yesterday told me the following anecdote:

‘I met yesterday (he said) a friend of mine whom I had not seen since I was at Oxford. That was some years ago and we had not, during all that time, had any communication with one another. Nor had we at Oxford any friends or acquaintances in common.

‘I was delighted to see my friend, nevertheless. “I suppose,” I said, “that lots of things have happened to you.”

‘”Why, yes,” was the answer. “I am married now and this is my little girl.”

‘I looked at the child — a pretty little thing of about six. “And what is your name, my dear,” I asked her. “Margaret,” was the reply. “Aha,” said I, “the same name as your mother’s.”‘

How did the speaker know?

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Black and White

jespersen chess problem

By Karl Lorenz Jesper Jespersen. White to mate in two moves.

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Parting Shot

http://commons.wikimedia.org/wiki/File:Samuel_Wilberforce_(1805%E2%80%931873),_Bishop_of_Oxford,_by_George_Richmond_1868.jpg

Bishop Samuel Wilberforce was fond of riddles. After his death in 1873, this one was found among his literary papers:

I’m the sweetest of sounds in Orchestra heard,
Yet in Orchestra never was seen.
I’m a bird of gay plumage, yet less like a bird,
Nothing ever in Nature was seen.
Touch the earth I expire, in water I die,
In air I lose breath, yet can swim and can fly;
Darkness destroys me, and light is my death,
And I only keep going by holding my breath.
If my name can’t be guessed by a boy or a man,
By a woman or girl it certainly can.

No one knows the answer.

07/05/2013 UPDATE: A great many readers have sent me proposed answers since I posted this item. The overwhelming favorite is “a whale” (or “orca”); others include “a woman’s voice” and “a soap bubble.” The latter was favored by Henry Dudeney (in his 300 Best Word Puzzles) — he, like everyone, is confident of his solution:

“We have no doubt that the correct answer is that we gave (apparently for the first time in print) in the Guardian for 6th February, 1920. This answer is the word BUBBLE. It is an old name for Bagpipes, the word exactly answers every line of the enigma, though the final couplet may be perplexing. The explanation is that ‘Bubble’ is an old name for breast.”