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.
A Russian problem from the 1999 Mathematical Olympiad:
In an election, each voter writes the names of n candidates on his ballot. Each ballot is then placed into one of n+1 boxes. After the election, it’s noted that each box contains at least one ballot, and that if one ballot is drawn from each box, these n+1 ballots will always have a name in common. Show that for at least one box, there’s a name that appears on all of its ballots.
A circular table stands in a corner, touching both walls. A certain point on the table’s edge is 9 inches from one wall and 8 inches from the other. What’s the diameter of the table?
In antiquity Aristotle had taught that a heavy weight falls faster than a light one. In 1638, without any experimentation, Galileo saw that this could not be true. What had he realized?
A logic exercise by Lewis Carroll: What conclusion can be drawn from these premises?
- No shark ever doubts that it is well fitted out.
- A fish that cannot dance a minuet is contemptible.
- No fish is quite certain that it is well fitted out unless it has three rows of teeth.
- All fishes except sharks are kind to children.
- No heavy fish can dance a minuet.
- A fish with three rows of teeth is not to be despised.
Longfellow thought that Dante Gabriel Rossetti, the Victorian poet and painter, was two different people. On leaving Rossetti’s house he said, “I have been very glad to meet you, Mr. Rossetti, and should like to have met your brother also. Pray tell him how much I admire his beautiful poem, ‘The Blessed Damozel.'”
In Philosophical Troubles, Saul A. Kripke offers a related puzzle. Peter believes that politicians never have musical talent. He knows of Paderewski, the great pianist and composer, and he has heard of Paderewski the Polish statesman, but he does not know that they are the same person. Does Peter believe that Paderewski had musical talent?
A riddle by Horatio Walpole:
Before my birth I had a name,
But soon as born I chang’d the same;
And when I’m laid within the tomb,
I shall my father’s name assume.
I change my name three days together
Yet live but one in any weather.
Another puzzle by Boris Kordemsky: Jack London tells of racing from Skagway, Alaska, to a camp where a friend lay dying. London drove a sled pulled by five huskies, which pulled the sled at full speed for 24 hours. But then two dogs ran off with a pack of wolves. Left with three dogs and slowed down proportionally, London reached the camp 48 hours later than he had planned. If the two lost huskies had remained in harness for 50 more miles, he would have been only 24 hours late. How far is the camp from Skagway?