Horse Sense

horse sense puzzle

From the U.K. Schools Mathematical Challenge, a multiple-choice competition for students ages 11-14:

Humphrey the horse at full stretch is hard to match. But that is just what you have to do: move one match to make another horse just like (i.e. congruent to) Humphrey. Which match must you move?

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Move A to become the new horse’s tail:

November 19, 2011January 29, 2013 | Puzzles

Catbird Seat

catbird seat 1

A ladder is leaning against a tree. On the center rung is a pussycat. She must be a very determined pussycat, because she remains on that rung as we draw the foot of the ladder away from the tree until the ladder is lying flat on the ground. What path does the pussycat describe as she undergoes this indignity?

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Perhaps surprisingly, she describes a quarter circle whose center is at the foot of the tree. As we draw out the ladder, essentially we’re creating a series of right triangles with the same hypotenuse (the ladder). The midpoint of the hypotenuse (the pussycat) will always maintain the same distance from all three vertices, including the right angle. Another way to see this is to remove the pussycat and visualize two ladders joined by a hinge at their midpoints. These make a scissoring motion as the first ladder descends, the second ladder drawing a simple circular arc whose center is at the base of the tree.

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November 16, 2011January 29, 2013 | Puzzles

The Footsoldier

fabel footsoldier chess puzzle - solution

By Karl Fabel, from Weltspiegel, 1946. White adds a pawn and mates in two moves.

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Add the pawn at h2. Then 1. h4 gxh4 e.p. (forced) 2. Bxg6 is mate:

November 15, 2011January 29, 2013 | Puzzles

Cut and Thrust

barbeau paper cutting puzzle - 1

University of Toronto math professor Ed Barbeau can take a rectangular piece of paper and, using only a pair of scissors, produce the object pictured above. How?

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Cut as shown along the vertical lines, then turn the right panel through 180 degrees. From Barbeau’s After Math: Puzzles and Brainteasers.

November 12, 2011January 29, 2013 | Puzzles

Black and White

loyd chess problem

By Sam Loyd. White to mate in two moves.

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1. Qa8 maintains the pin on the black queen from a safe distance. If she moves, then Bh2#. If 1. … h2, then 2. Qxg2#. From the Baltimore Herald, 1880.

November 7, 2011January 29, 2013 | Puzzles

Noted

A riddle from 1655:

What is likest to a cat in a hole?

A cat out of a hole.

See Poser.

November 5, 2011November 4, 2011 | Puzzles

Sound Sense

Here is a class of a dozen boys, who, being called up to give their names were photographed by the instantaneous process just as each one was commencing to pronounce his own name. The twelve names were Oom, Alden, Eastman, Alfred, Arthur, Luke, Fletcher, Matthew, Theodore, Richard, Shirmer, and Hisswald. Now it would not seem possible to be able to give the correct name to each of the twelve boys, but if you practice the list over to each one, you will find it not a difficult task to locate the proper name for every one of the boys.

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Out of the thousands of persons who were interested in the scientific feature of that curious lip-reading puzzle the ease and unanimity with wich they picked out little Matthew as the first boy on the top row encouraged them to tackle the next, and by a large majority Matthew, Alfred and Eastman were located on the top row, Richard, Theodore, Luke and Oom on the second row, with Hisswald, Shirmer, Fletcher, Arthur and Alden below. From the many correct answers received it would appear to be an easier feat to read the motion of the lips than one would suppose.

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November 1, 2011January 29, 2013 | Puzzles

Four Puzzles

You’re playing bridge. Each of four players is dealt 13 cards. You and your partner find that between you you hold all 13 cards of one suit. Is this more or less likely than that the two of you hold no cards of one suit?
As he left a restaurant, a man gave the cashier a card bearing the number 102004180. The cashier charged him nothing. Why?
How can you position a marble on the floor of an empty room so that I can’t hit it with a baseball?
Thrice what number is twice that number?

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The two events are equivalent — if two players lack all cards of a given suit, then the other two players hold all of them. 102004180 means “I ought to owe nothing for I ate nothing.” Put it in the corner. Zero.

October 31, 2011January 29, 2013 | Puzzles

Crime Scene

mortimer chess puzzle

A tricky problem by Ernest Clement Mortimer. This position was reached after Black’s fourth move in a legal chess game. Can you reconstruct the game?

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The trick is that the knight on b8 began on g8: 1. Nf3 d5 2. Ne5 Nf6 3. Nc6 Nfd7 4. Nxb8 Nxb8 This is the only way this position can be reached in four moves.

October 29, 2011January 29, 2013 | Puzzles

Installment Plan

A traveler wants to stay at an inn for seven days. He has no money, but he has a gold chain with seven links. The innkeeper agrees to accept this in payment for the week’s stay, but the traveler is reluctant to part with all seven links at once. He prepares to cut the chain into seven pieces.

The innkeeper stops him. If the traveler is willing occasionally to accept change in the form of links previously paid, then they can work out a plan that minimizes damage to the chain and yet permits the traveler to pay only what he owes on each successive day. How many links must they cut?

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They cut a single link, the third one, dividing the chain into lengths of 1, 2, and 4. Now: On day 1 the traveler gives the innkeeper 1 link. On day 2 the traveler gives the innkeeper 2 links and accepts 1 in return. On day 3 the traveler gives the innkeeper 1 link. On day 4 the traveler gives the innkeeper 4 links and accepts 3 in return. On day 5 the traveler gives the innkeeper 1 link. On day 6 the traveler gives the innkeeper 2 links and accepts 1 in return. On day 7 the traveler gives the innkeeper 1 link. (In effect they’re counting in base 2.)

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October 28, 2011January 29, 2013 | Puzzles