## Three Riddles

From Henry Dudeney’s *300 Best Word Puzzles*:

- What is that from which you may take away the whole and yet have some left?
- What is it which goes with an automobile, and comes with it; is of no use to it, and yet the automobile cannot move without it?
- Take away my first letter and I remain unchanged; take away my second letter and I remain unchanged; take away my third letter and I remain unchanged; take away all my letters and still I remain exactly the same.

## Pillow Talk

In 1951 James Thurber’s friend Mitchell challenged him to think of an English word that contains the four consecutive letters SGRA. Lying in bed that night, Thurber came up with these:

*kissgranny*. A man who seeks the company of older women, especially older women with money; a designing fellow, a fortune hunter.

*blessgravy*. A minister or cleric; the head of a family; one who says grace.

*hossgrace*. Innate or native dignity, similar to that of the thoroughbred hoss.

*bussgranite*. Literally, a stonekisser; a man who persists in trying to win the favor or attention of cold, indifferent, or capricious women.

*tossgravel*. A male human being who tosses gravel, usually at night, at the window of a female human being’s bedroom, usually that of a young virgin; hence, a lover, a male sweetheart, and an eloper.

Unfortunately, none of these is in the dictionary. What word was Mitchell thinking of?

## 15 Puzzle

A problem from the 1999 Russian mathematical olympiad:

Show that the numbers from 1 to 15 can’t be divided into a group A of 13 numbers and a group B of 2 numbers so that the sum of the numbers in A equals the product of the numbers in B.

## Cold Case

*Enigma*, the official publication of the National Puzzlers’ League, published this item in the “Chat” column of its August 1916 issue:

“The police department of Lima, O., is greatly puzzled over a cryptic message received in connection with the robbery of a Western Ohio ticket agent. Here it is: WAS NVKVAFT BY AAKAT TXPXSCK UPBK TXPHN OHAY YBTX CPT MXHG WAE SXFP ZAV FZ ACK THERE FIRST TXLK WEEK WAYZA WITH THX.”

As far as I can tell, in the ensuing 97 years it has never been solved. Any ideas?

## In a Word

carfax

n. a place where four roads meet

Traveling between country towns, you arrive at a lonely crossroads where some mischief-maker has uprooted the signpost and left it lying by the side of the road.

Without help, how can you choose the right road and continue your journey?

## A Martian Census

A room contains more than one Martian. Each Martian has two hands, with at least one finger on each hand, and all Martians have the same number of fingers. Altogether there are between 200 and 300 Martian fingers in the room; if you knew the exact number, you could deduce the exact number of Martians. How many Martians are there, and how many fingers does each one have?

## 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?

## Alcohol Problem

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.

## 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?

## 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?

## 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.

## 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!)

## Coverup

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

## 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.