Black and White

marache chess problem

By N. Marache. White to mate in two moves.

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1. Re6! and the bishop will mate.

February 3, 2012January 31, 2013 | Puzzles

Popularity Contest

Prove that at least two Welshmen have the same number of Welsh friends.

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Well, suppose they don’t. If there are n Welshmen in the world, each can have any number of Welsh friends from 0 to n-1 (he can’t be friends with himself). If we are to arrange things so that no two Welshmen have the same number of friends, then the first must have 0 friends, the next 1 friend, and so on. But then the loneliest Welshman has no friends and the most popular is friends with every Welshman but himself. This is a contradiction. Hence there must be some overlap — at least two Welshmen must have the same number of friends. This is essentially the same idea as in Hand Count. I think it appeared originally in the Litton Problematical Recreations series.

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January 30, 2012January 31, 2013 | Puzzles

Yar

Three pirates find themselves on an island with a chest full of miscellaneous treasure. They have no weighing or measuring equipment. How can they divide the loot to the satisfaction of each?

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Pirate A picks out what he thinks is a third of the loot. Pirates B and C, in turn, have the option of returning some of it to the chest. In effect, each is making a bid as to the smallest “third” that he’s willing to accept. The last one to make a proposal (which might be Pirate A himself) keeps this first portion for himself. The other two pirates then split the remaining treasure in the conventional way: one divides it into two portions and the other chooses between them.

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January 29, 2012January 31, 2013 | Puzzles

Black and White

By T.M. Brown. White to mate in two moves.

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1. Bd1 Kxb1 2. Bb3#

January 28, 2012January 31, 2013 | Puzzles

In a Word

nepotal
adj. relating to a nephew

“That is my nephew,” said a man to his sister.

“He is not my nephew,” she said.

How is this possible?

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The boy is her son.

January 26, 2012January 30, 2013 | Language · Puzzles

Even Odds

A bag contains 16 billiard balls, some white and some black. You draw two balls at the same time. It is equally likely that the two will be the same color as different colors. What is the proportion of colors within the bag?

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The obvious answer, that there are eight balls of each color, doesn’t quite work: Of the 120 possible pairs drawn from such a bag, 64 have one ball of each color (8 white balls × 8 black balls) and 56 have two of the same color (28 possible pairs of white balls + 28 possible pairs of black balls). That gives a probability of 64/120 = 0.53 of getting a mixed draw and 56/120 = 0.47 of getting two balls of the same color. But if the bag contains 6 balls of one color and 10 of the other, then there are 60 ways of getting a mixed draw, 45 ways of drawing the more common color, and 15 ways of drawing the less common color. 60 = 45 + 15, so the two outcomes are equally likely.

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January 22, 2012January 30, 2013 | Puzzles · Science & Math

Black and White

By Joseph A. Potter. White to mate in two moves.

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1. Nc8 Kxc8 2. Qa8#

January 21, 2012January 30, 2013 | Puzzles

Vision Thing

A puzzle from Lewis Carroll:

A king wishes to dismiss his wise men, but he must obey an old law that says there must always be:

Seven blind of both eyes,
Ten blind of one eye,
Five that see with both eyes,
Nine that see with one eye.

How many wise men must he keep?

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Carroll’s answer: Five seeing, and seven blind Give us twelve, in all, we find; But all of these, ’tis very plain, Come into account again. For take notice, it may be true, That those blind of one eye are blind for two; And consider contrariwise, That to see with your eye you may have your eyes; So setting one against the other — For a mathematician no great bother — And working the sum, you will understand That sixteen wise men now trouble the land.

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January 20, 2012January 30, 2013 | Puzzles

Black and White

amusing old timer chess problem

The British Chess Magazine reprinted this “amusing old timer” in 1892. “We suspect that the amusement will be caused by the rapidity of solving it, and the prettiness and surprise of the mating position.” White to mate in two moves.

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1. Qf3+!! Kxf3+ 2. Ne5#

January 14, 2012January 30, 2013 | Puzzles

Pool Party

A billiard ball is resting on a table that measures 10 feet by 5 feet. A player hits it with no “English” and it strikes four different cushions and returns to its starting point. University of Alberta mathematician Murray Klamkin asks: How far did it travel?

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The ball’s path can be drawn as a straight line (green) across a field of mirrored tables. It strikes four cushions and returns to its original position on the table. Its starting and ending positions (the endpoints of the green line) can be connected to a corner of the table by lines that are parallel and equal (yellow). If we complete the parallelogram (blue), it becomes clear that the ball’s path is equal in length to two of the table’s diagonals, or about 22.36 feet.

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January 8, 2012January 30, 2013 | Puzzles