## Project Management

A puzzle by Polish mathematician Paul Vaderlind:

If a blacksmith requires five minutes to put on a horseshoe, can eight blacksmiths shoe 10 horses in less than half an hour? The catch: A horse can stand on three legs, but not on two.

## Swine Wave

A bewildering puzzle by Lewis Carroll: Place 24 pigs in these sties so that, no matter how many times one circles the sties, he always find that the number in each sty is closer to 10 than the number in the previous one.

## Belt Loop

A puzzle by Harry Langman:

A thin belt is stretched around three pulleys, each of which is 2 feet in diameter. The distances between the centers of the pulleys are 6 feet, 9 feet, and 13 feet. How long is the belt?

## No Answer

Helen Fouché Gaines’ 1956 textbook *Cryptanalysis: A Study of Ciphers and Their Solution* concludes with a cipher that, she says, “nobody has ever been able to decrypt”:

VQBUP PVSPG GFPNU EDOKD XHEWT IYCLK XRZAP VUFSA WEMUX GPNIV QJMNJ JNIZY KBPNF RRHTB WWNUQ JAJGJ FHADQ LQMFL XRGGW UGWVZ GKFBC MPXKE KQCQQ LBODO QJVEL.

It was still unsolved in 1968, when Dmitri Borgmann, editor of the *Journal of Recreational Linguistics*, urged his readers to tackle the problem: “Are you going to let this challenge lie there, taunting you for the rest of your lives? Or are you going to get busy and solve that pesky little crypt?”

So far as I can tell, they let it lie there, and it remains unsolved to this day. Any ideas? There are few clues in Gaines’ book. The cipher is the last in a series of exercises at the end of a chapter titled “Investigating the Unknown Cipher,” and she gives no hint as to its source. Of the exercises, she writes, “There is none in which the system may not be learned through analysis, unless perhaps the final unnumbered cryptogram.” The solution says simply “Unsolved.”

## Pillow Problem

From a 1921 essay by A.A. Milne:

TERALBAY is not a word which one uses much in ordinary life. Rearrange the letters, however, and it becomes such a word. A friend — no, I can call him a friend no longer — a person gave me this collection of letters as I was going to bed and challenged me to make a proper word of it. He added that Lord Melbourne — this, he alleged, is a well-known historical fact — Lord Melbourne had given this word to Queen Victoria once, and it had kept her awake the whole night. After this, one could not be so disloyal as to solve it at once. For two hours or so, therefore, I merely toyed with it. Whenever I seemed to be getting warm I hurriedly thought of something else. This quixotic loyalty has been the undoing of me; my chances of a solution have slipped by, and I am beginning to fear that they will never return. While this is the case, the only word I can write about is TERALBAY.

The answer is not RATEABLY, or BAT-EARLY, which “ought to mean something, but it doesn’t.” Rudolf Flesch notes that TRAYABLE is not a word, and that, though TEARABLY appears in small type in *Webster’s Unabridged*, “it obviously won’t do.”

What’s the answer? There’s no trick — it’s an ordinary English word.

## Hole Hearted

Martin Gardner called this the proudest puzzle of his own devising. When the pieces on the left are rearranged as on the right, a hole appears in the center of the square. How is this possible?

“I haven’t the foggiest notion of how to succeed in inventing a good puzzle,” he told the *College Mathematics Journal*. “I don’t think psychologists understand much either about how mathematical discoveries are made. … The creative act is still a mystery.”

## Set Theory

A puzzle by Polish mathematician Paul Vaderlind:

Andre Agassi and Boris Becker are playing tennis. Agassi wins the first set 6-3. If there were 5 service breaks in the set, did Becker serve the first game?

(Service changes with each new game in the 9-game set. A service break is a game won by the non-server.)

## Black and White

By Werner Keym, from *Die Schwalbe*, 1979. What were the last moves by White and Black?

## The Lock Key

Two adjoining lakes are connected by a lock. The lakes differ by 2 meters in elevation. A boat can pass from the lower lake to the upper by passing through the lock gate, which is closed behind it; then water is added to the lock chamber until its level matches that of the upper lake, and the boat can pass out through the upper gate.

Now suppose two boats do this in succession. The first boat weighs 50 tons, the second only 5 tons. How much more water must be used to raise the small boat than the large one?

## No Touching

This scale balances a cup of water with a certain weight. Will the balance be upset if you put your finger in the water, if you’re careful not to touch the glass?

## Black and White

A curious puzzle by George Koltanowski, from *America Salutes Comins Mansfield*, 1983. “Who mates in 1?”

## Counter Play

A puzzle by Lewis Carroll:

A bag contains one counter, known to be either white or black. A white counter is put in, the bag shaken, and a counter drawn out, which proves to be white. What is now the chance of drawing a white counter?

## Spear Fight

A puzzle by Henry Dudeney:

A lady is accustomed to buy from her greengrocer large bundles of asparagus, each twelve inches in circumference. The other day the man had no large bundles in stock, but handed her instead two small ones, each six inches in circumference. “That is the same thing,” she said, “and, of course, the price will be the same.” But the man insisted that the two bundles together contained more than the large one, and charged a few pence extra. Which was correct — the lady or the greengrocer?

## Black and White

Raymond Smullyan presented this puzzle on the cover of his excellent 1979 book *The Chess Mysteries of Sherlock Holmes*. Black moved last. What was his move?

## Lazy Tennis

You’ve just won a set of singles tennis. What’s the least number of times your racket can have struck the ball? Remember that if you miss the ball while serving, it’s a fault.

## Twisted Math

The Renaissance mathematician Niccolò Tartaglia would use this bewildering riddle to assess neophytes in logic:

If half of 5 were 3, what would a third of 10 be?

What’s the answer?

## Stride Right

A mother takes two strides to her daughter’s three. If they set out walking together, each starting with the right foot, when will they first step together with the left?