Caller ID

In his 1936 collection Brush Up Your Wits, British puzzle maven Hubert Phillips relates that his brother-in-law felt himself cursed with an unintelligent maid. “I have just overheard her taking a ‘phone call,” he told Phillips, “and this is what I heard:

“‘Is Mr. Smith at home?’

“‘I will ask him, sir. What name shall I give him?’

“‘Quoit.’

“‘What’s that, sir?’

“‘Quoit.’

“‘Would you mind spelling it?’

“‘Q for quagga, U for umbrella, O for omnibus, I for idiot –‘

“‘I for what, sir?’

“‘I for idiot, T for telephone. Q, U, O, I, T, Quoit.’

“‘Thank you, sir.'”

Why did he accuse her of unintelligence?

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Because, having understood that the fourth letter was I, she had no need to confirm what the I stood for.

November 14, 2013November 22, 2013 | Puzzles

Brood War

A newlywed couple are planning their family. They’d like to have four children, a mix of girls and boys. Which is more likely: (1) two girls and two boys or (2) three children of one sex and one of the other? (Assume that each birth has an equal chance of being a boy or a girl.)

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Most people guess that (1) is more likely, but in fact (2) is. There are 16 possible arrangements: BBBB GBBB BGBB BBGB BBBG GGBB GBGB GBBG BGGB BGBG BBGG GGGB GGBG GBGG BGGG GGGG Eight of these have three children of one sex and one of the other; only six have two brothers and two sisters.

November 10, 2013November 15, 2013 | Puzzles

Black and White

meredith chess problem

By William Meredith. White to mate in two moves.

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Black’s king is immobilized; his h6 knight must maintain its guard against Nxf7#; and moving his pawn would permit Rh7# (or Nxg6#). That means that only the e4 knight is free to move safely. With 1. Qb1! white immobilizes that piece as well, as moving it would now permit 2. g7#, since the queen now guards the king’s only escape square. So Black is out of safe moves, and must invite a mate. From Checkmate, 1901.

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November 8, 2013November 15, 2013 | Puzzles

Flip Sum

A problem from the 1999 St. Petersburg City Mathematical Olympiad:

Fifty cards are arranged on a table so that only the uppermost side of each card is visible. Each card bears two numbers, one on each side. The numbers range from 1 to 100, and each number appears exactly once. Vasya must choose any number of cards and flip them over, and then add up the 50 numbers now on top. What’s the highest sum he can be sure to reach?

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The highest number he can be sure to reach is (1/2)(1 + 2 + 3 + … + 100), or 2525. If the visible numbers already meet this total, he should accept them as they are; otherwise he should flip all 50 cards. This might be the best that he can do. Suppose that the cards show the numbers from 26 to 75 (totaling 2525) and that the k cards he flips over are the first k cards in the sequence 1, 2, …, 25, 76, 77, …, 100. If he flips over fewer than 26 cards his sum will decrease; if he flips more than that, the sum will rise again but will reach 2525 only with the 50th card. Either way, he won’t beat that total.

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November 7, 2013November 15, 2013 | Puzzles

Black and White

larsen chess problem

By Peder Andreas Larsen. White to mate in two moves.

(I’ve added a guide to chess notation.)

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White wins with the ridiculous 1. Qg1!, threatening 2. N4b6#. If Black moves his bishop, then 2. Qa7 is mate, and if Black advances his b-pawn, then the queen takes the rook. From Skakbladet, 1918.

November 1, 2013November 8, 2013 | Puzzles

Black and White

By Francis Healey. White to mate in two moves.

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1. Qa7! and the queen or rook will mate. From A Collection of Two Hundred Chess Problems, 1866.

October 25, 2013November 1, 2013 | Puzzles

Square Deal

square deal puzzle

A puzzle by Sam Loyd. The red strips are twice as long as the yellow strips. The eight can be assembled to form two squares of different sizes. How can they be rearranged (in the plane) to form three squares of equal size?

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October 23, 2013January 30, 2022 | Puzzles

Black and White

møller chess problem

By Jørgen Thorvald Møller. White to mate in two moves.

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1. Kf6! and White will mate with 2. Qh1# or 2. Kg6#. From Skakbladet, August 1919.

October 18, 2013October 25, 2013 | Puzzles

All Relative

A problem from Dick Hess’ All-Star Mathlete Puzzles (2009):

A man points to a woman and says, “That woman’s mother-in-law and my mother-in-law are mother and daughter (in some order).” Name three ways in which the two can be related.

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The woman can be the man’s daughter-in-law, because his wife is the daughter of his mother-in-law. The woman can be the man’s wife’s aunt (his mother-in-law’s brother’s wife), because his mother-in-law is the daughter of her own brother’s wife’s mother-in-law. The woman can be the wife of the man’s nephew (the wife of his wife’s sister’s son), because his wife is the daughter of his mother-in-law. Equivalently, the man can be the woman’s father-in-law, her niece’s husband (her husband’s sister’s daughter’s husband), or her aunt’s husband (her husband’s mother’s sister’s husband).

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