“A Cube Paradox”

dudeney cube puzzle

A puzzle from Henry Dudeney:

I had two solid cubes of lead, one very slightly larger than the other, just as shown in the illustration. Through one of them I cut a hole (without destroying the continuity of its four sides) so that the other cube could be passed right through it. On weighing them afterwards it was found that the larger cube was still the heavier of the two! How was this possible?

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“Cutting the Cheese”

cutting the cheese

A puzzle from Henry Ernest Dudeney:

Here is a simple question that will require just a few moments’ thought to get an exact answer. I have a piece of cheese in the shape of a cube. How am I to cut it in two pieces with one straight cut of the knife so that the two new surfaces produced by the cut shall each be a perfect hexagon? Of course, if cut in the direction of the dotted line the surfaces would be squares. Now produce hexagons.

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Card Trick


Take … a common visiting-card, and bend down the two ends, and place it on a smooth table, as represented in the annexed diagram, and then ask any one to blow it over.

This seems easy enough; yet it is next door to an impossibility. Still, it is to be done by blowing sharply and not too hard on the table, about an inch from the card.

— Frank Bellew, The Art of Amusing, 1866

“To Take a Man’s Waistcoat Off Without Removing His Coat”

The waistcoat should first be unbuttoned in the front, and then the buckle at the back must be unloosed. The operator, standing in front of the person operated upon, should then place his hands underneath the coat at the back, taking hold of the bottom of the waistcoat, at the same time requesting the wearer to extend his arms at full length over his head. Now raise the bottom part of the waistcoat over the head of the wearer (if the waistcoat be tight it will be necessary to force it a little, but this must not be minded so long as the waistcoat is not torn); the waistcoat then will have been brought to the front of the wearer, across his chest. Take the right side bottom-end of the waistcoat, and put it into the arm-hole of the coat at the shoulder, at the same time putting the hand up the sleeve, seizing the end, and drawing it down the sleeve; this action will release one arm-hole of the garment to be removed. The next thing to be done is to pull the waistcoat back again out of the sleeve of the coat, and put the same end of the waistcoat into the left arm-hole of the coat, again putting the hand up the sleeve of the coat as before, and seizing the end of the garment. It may then be drawn quite through the sleeve, and the puzzle is accomplished.

Cassell’s Complete Book of Sports and Pastimes, 1896

The Locked Gift


I want to mail a necklace to my wife, but anything sent through the mail will be stolen unless it’s sent in a padlocked box. A box can bear any number of padlocks, but neither of us has the key to a lock owned by the other. How can I mail the necklace safely to my wife?

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“Monkey and Pulley”

A rope is passed over a pulley. It has a weight at one end and a monkey at the other. There is the same length of rope on either side and equilibrium is maintained. The rope weighs four ounces per foot. The age of the monkey and the age of the monkey’s mother together total four years. The weight of the monkey is as many pounds as the monkey’s mother is years old. The monkey’s mother is twice as old as the monkey was when the monkey’s mother was half as old as the monkey will be when the monkey is three times as old as the monkey’s mother was when the monkey’s mother was three times as old as the monkey. The weight of the rope and the weight at the end is half as much again as the difference in weight between the weight of the weight and the weight and the weight of the monkey. Now, what is the length of the rope?

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“Cupid’s Arithmetic”

A conundrum from Henry Ernest Dudeney, Modern Puzzles, 1926:

Dora Crackham one morning produced a slip of paper bearing the jumble of figures shown in our illustration. She said that a young mathematician had this poser presented to him by his betrothed when she was in a playful mood.

cupid's arithmetic

“What am I to do with it?” asked George.

“Just interpret its meaning,” she replied. “If it is properly regarded it should not be difficult to decipher.”

What did she mean?

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Kavka’s Toxin Puzzle

I’ll give you a million dollars if you intend to drink this poison.

You don’t actually have to drink it. I’ll pay you immediately, and then you’re perfectly free to change your mind.

Can you do this?

(Posed by University of California political philosopher Gregory Kavka.)

King, Queen, Knave

nabokov chess problem

Vladimir Nabokov composed chess problems. Here’s a clever one from 1932: “White retracts its last move and mates in one.”

This is an instance of retrograde analysis: Of the many legal moves that White might just have made, only one can be revised to yield an immediate mate. Can you find it?

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Measured Steps

Twenty-five ants are placed randomly on a meter stick. Each faces east or west. At a signal they all start to march at 1 centimeter per second. Whenever two ants collide they reverse directions. How long must we wait to be sure that all the ants have left the stick?

This sounds immensely complicated, but with a simple insight the answer is immediately clear. What is it?

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