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?’
“‘What’s that, sir?’
“‘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?
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.)
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?
By Peder Andreas Larsen. White to mate in two moves.
(I’ve added a guide to chess notation.)
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?
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.