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.

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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?

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Round and Round

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?”

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

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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?”

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The Missing Footmen

Like Nabokov, Lord Dunsany was fond of composing chess problems. This example was published in Hubert Phillips’ Week-end Problems Book of 1932:

dunsany - the missing footmen chess problem - 1

Two eccentric gentlemen abandoned this position at a chess club — White had announced mate in four. What was the mate?

The key is to notice that Black’s king and queen have changed positions. This is not possible if the black pawns are on their home squares. And this means that we’ve been viewing the position upside down:

dunsany - the missing footmen chess problem - 2

Now it’s clear that Black is hemmed in by his own pawns — White can mate him in four moves with the b8 knight, e.g. by 1. Nc6 Nf3 2. Nb4 (threatening Nd3#) Ne5 3. Qxe5 (any) 4. Nd3#.

Dunsany drew a game against Capablanca in a simultaneous exhibition in London in April 1929. He later wrote:

One art they say is of no use;
The mellow evenings spent at chess,
The thrill, the triumph, and the truce
To every care, are valueless.

And yet, if all whose hopes were set
On harming man played chess instead,
We should have cities standing yet
Which now are dust upon the dead.

Gender Issues

In a certain kingdom, boys and girls are born in strictly equal proportions. Determined to increase the proportion of women in the land, the sultan issues a decree: Any woman who bears a son is forbidden to have any further children. He reasons that some families will thus contain multiple daughters but a single son.

A number of years pass, and the sultan is confused to find that the kingdom still contains an equal number of boys and girls. Why?

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The Motor Hire

A puzzle from R.M. Abraham, Diversions & Pastimes, 1933:

Michael O’Bleary hired a motor-car at a cost of fifteen dollars to take him to Ballygoogly market and back again in the evening. When he got half-way on his outward journey he met a friend, gave him a lift to the market, and brought him back to the point where he picked him up in the morning. There was a dispute about the payment. How much should Michael charge his passenger for his share of the motor hire?

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