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Stairway to Seven

You hate visiting your girlfriend because there’s no elevator in her apartment building. And now she’s moved from the fourth floor to the seventh. How many times longer does this make your ascent?

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His and Hers

Many masculine nouns can be converted to feminine with a suffix, as HERO-HEROINE and HOST-HOSTESS.

Name a feminine noun that can be converted to masculine with a suffix.

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Open and Shut


Every room in my house has an even number of doors.

Prove that the house has an even number of exterior doors.

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Track Meet

One train leaves Los Angeles for New York at 60 mph.

At the same time, another train leaves New York for Los Angeles at 40 mph.

What is the distance between them one hour before they meet?

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Who’s Laughing Now?

A.A. Bennett offered this puzzle in the American Mathematical Monthly of May 1937:

A car with n (n > 2) passengers of different speeds of mental reaction passes through a tunnel and each passenger acquires unconsciously a smudge of soot upon his forehead. Suppose that each passenger

(1) laughs and continues to laugh as soon as and only so long as he sees a smudge upon the forehead of a fellow passenger;
(2) can see the foreheads of all his fellows;
(3) reasons correctly;
(4) will clean his own forehead when and only when his reasoning forces him to conclude that he has a smudge;
(5) knows that (1), (2), (3), and (4) hold for each of his fellows.

Show that each passenger will eventually wipe his own forehead.

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Formal Speech

A puzzle by Isaac Asimov:

What word in the English language changes its pronunciation when it is capitalized?

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The Mail Plane

A motorcyclist was sent by the post office to meet a plane at the airport.

The plane landed ahead of schedule, and its mail was taken toward the post office by horse. After half an hour the horseman met the motorcyclist on the road and gave him the mail.

The motorcyclist returned to the post office 20 minutes earlier than he was expected.

How many minutes early did the plane land?

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A Geometry Problem

A poser from 1821:

Mathematicians affirm that of all bodies contained under the same superficies, a sphere is the most capacious: But they have never considered the amazing capaciousness of a body, the name of which is now required, of which it may be truly affirmed, that supposing its greatest length 9 inches, greatest breadth 4 inches, and greatest depth 3 inches, yet under these dimensions it contains a solid foot?

What is this body?

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The Card Challenge

A problem posed by Harry Houdini: Given a piece of cardboard measuring 4″ × 2.5″, cut it so that a person can pass completely through it without tearing it.

Can it be done?

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“A Crime Story”

From the American journal Scripta Mathematica:

An elementary school teacher in New York state had her purse stolen. The thief had to be Lilian, Judy, David, Theo, or Margaret. When questioned, each child made three statements:

(1) I didn’t take the purse.
(2) I have never in my life stolen anything.
(3) Theo did it.

(4) I didn’t take the purse.
(5) My daddy is rich enough, and I have a purse of my own.
(6) Margaret knows who did it.

(7) I didn’t take the purse.
(8) I didn’t know Margaret before I enrolled in this school.
(9) Theo did it.

(10) I am not guilty.
(11) Margaret did it.
(12) Lillian is lying when she says I stole the purse.

(13) I didn’t take the teacher’s purse.
(14) Judy is guilty.
(15) David can vouch for me because he has known me since I was born.

Later, each child admitted that two of his statements were true and one was false. Assuming this is true, who stole the purse?

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A Riding Tour

a riding tour

Is it possible to move the knight from a1 to h8, visiting every square of the chessboard once?

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  1. Which is worth more, a pound of $10 gold pieces or half a pound of $20 gold pieces?
  2. A kazoo costs $1 plus half its price. How much does it cost?
  3. On its March 1961 cover, MAD Magazine pointed out that 1961 was the first “upside-up” year — the first year that reads the same upside down — since 1881. What will be the next such year?
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The Stopped Clock

Andrea’s only timepiece is a clock that’s fixed to the wall. One day she forgets to wind it and it stops.

She travels across town to have dinner with a friend whose own clock is always correct. When she returns home, she makes a simple calculation and sets her own clock accurately.

How does she manage this without knowing the travel time between her house and her friend’s?

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You’re given a choice between two gifts: $5 and $1,000. You can choose either, but a bystander will give you $1 million if you choose irrationally. Can you do it?

See also Kavka’s Toxin Puzzle.

Find the Theme, Part 2

What do these words have in common?

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Hell’s Bells

hell's bells

A Christmas puzzle by J.C.J. Wainwright, from the American Chess Bulletin, December 1917.

White to mate in one move.

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Retail Trouble

A woman visits a jewelry store and buys a ring for $100.

The next day she returns and asks to exchange it for another. She picks out one worth $200, thanks the jeweler and turns to go.

“Wait, miss,” he says. “That’s a $200 ring.”

“Yes,” she says. “I paid you $100 yesterday, and I’ve just given you a ring worth $100.”

And she trips lightly out of the store.

The Corpse Groom

A man once married his widow’s sister.

How is this possible?

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By Sam Loyd. In how few moves can White mate?

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Find the Theme, Part 1

What do these words have in common?

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Nepotism Rewarded

It’s your first day at XYZ Industries, and your new boss calls you into his office. There you meet another trainee, J. Wellington Smithersby-Farquhar VII, the owner’s son, who is already helping himself to the brandy.

“Gentlemen,” says the boss, “we have a bit of a difficulty. You’ll both be starting at $100,000 per year, as promised. But I must offer you different increases. One of you will get a $15,000 raise each year, and the other a $5,000 raise every half-year.”

“That’s no problem, sir,” says Wellington, lighting a cigar. “I’m sure Jenkins will be quite happy with the smaller sum.”

The boss coughs uncomfortably. “Jenkins,” he says, “is that acceptable?”

How should you respond?

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By Karl Fabel. White to move and not checkmate.

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Royal Pain

You’re a knight in love with a princess. Unfortunately, the king knows you’re poor and disapproves of the match.

On the night of a great feast, the king calls you up before his men and presents a golden box. In it are two folded slips of paper. One, he announces, reads “Marriage,” the other “Death.” “Choose one,” he says.

Pretending to stir the fire, the princess manages to whisper that both slips say “Death.” But the king and his men are waiting, and you cannot escape now.

What should you do?

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Rock and Roll

Worshipful natives are rolling a giant statue of me across their island. The statue rests on a slab, which rests on rollers that have a circumference of 1 meter each. How far forward will the slab have moved when the rollers have made 1 revolution?

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