Door Jam

You’re confronted with two doors. One leads to fortune, the other to death, but you don’t know which is which.

The doors are attended by two guards. One always lies, and the other always tells the truth, but again you don’t know which is which.

You can ask one question of one guard. What should you ask?

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Ask either guard, “Which door would the other guard advise me to take?” The truth-telling guard will honestly indicate the bad door, and the lying guard will falsely indicate the bad door. Either way, you’re safe in taking the opposite door. A sequel, from John Finnemore’s Souvenir Programme:

February 7, 2012January 31, 2013 | Puzzles

Spirit Reading

In a certain town, 90 percent of the residents drink coffee, 80 percent drink tea, 70 percent drink whiskey, and 60 percent drink gin. No one drinks all four. What percent of the residents drink liquor?

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Let C be the set of residents who drink coffee and C′ the set who don’t, and so on. So C′ contains 10 percent of the residents, T′ 20 percent, W′ 30 percent, and G′ 40 percent. Because every resident abstains from something, these four segments must cover 100 percent of the population. And because the four segments just total 100 percent, there can be no overlap among them. Hence every resident drinks three of the four beverages, and 100 percent drink liquor.

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February 6, 2012January 31, 2013 | Puzzles

Economical

A baseball pitcher played an entire game while throwing the minimum possible number of pitches. The game was not called before completion. How many pitches did he throw?

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Twenty-five. He could avoid pitching in the ninth inning if his team lost. But in order to lose he must have allowed at least one run, and that would require at least one pitch. Twenty-four additional pitches produced three outs in each of eight innings, for a total of 25 pitches. 02/06/2012 UPDATE: I found this problem in the Litton Problematical Recreations series, but as many of you have pointed out, the answer is wrong. Technically there are at least two ways in which a pitcher can complete a game without throwing a single pitch: — Rule 8.04 says that if a pitcher fails to deliver the ball within 12 seconds of receiving it, the umpire can call a ball. A very dilatory pitcher could put 27 men on base in this way and then pick them all off. — If the pitcher plays right field, he won’t pitch at all. :) Thanks for everyone who wrote in about this.

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February 5, 2012January 31, 2013 | Puzzles

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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