A puzzle from Russia:
Draw two straight lines on the clock face so that the sums of the numbers in each part are equal.
Four missiles are located in the corners of a square 20 miles on each side. All are launched simultaneously, and each homes in on the one on its left at 1 mile per second. How much time will pass before they meet?
From Lewis Carroll’s first textbook in symbolic logic:
- No kitten that loves fish is unteachable.
- No kitten without a tail will play with a gorilla.
- Kittens with whiskers always love fish.
- No teachable kitten has green eyes.
- No kittens have tails unless they have whiskers.
What conclusion can be drawn from these premises?
A bewildering riddle by the English statesman Charles James Fox (he of the widely spaced aunts):
I went to the Crimea; I stopped there, and I never went there, and I came back again. What am I?
Well, you’ve gone and murdered someone again. And this time you’ve done it in Elephantistan, which is renowned for its peculiar justice system.
The jury is divided, so you will decide your own fate. You’re presented with two urns, each of which contains 25 white balls and 25 black ones. Blindfolded, you must choose an urn at random and then draw a ball from it; a black ball means death, but a white one means you go free.
Tradition gives you the option to distribute the balls however you like between the two urns before you don the blindfold. This is thought to be a formality, as the total proportion of white balls to black does not change.
What should you do?
A riddle by Jonathan Swift:
By something form’d, I nothing am,
Yet everything that you can name;
In no place have I ever been,
Yet everywhere I may be seen;
In all things false, yet always true,
I’m still the same–but ever new.
Lifeless, life’s perfect form I wear,
Can shew a nose, eye, tongue, or ear,
Yet neither smell, see, taste, or hear.
All shapes and features I can boast,
No flesh, no bones, no blood–no ghost:
All colours, without paint, put on,
And change like the cameleon.
Swiftly I come, and enter there,
Where not a chink lets in the air;
Like thought, I’m in a moment gone,
Nor can I ever be alone:
All things on earth I imitate
Faster than nature can create;
Sometimes imperial robes I wear,
Anon in beggar’s rags appear;
A giant now, and straight an elf,
I’m every one, but ne’er myself;
Ne’er sad I mourn, ne’er glad rejoice,
I move my lips, but want a voice;
I ne’er was born, nor e’er can die,
Then, pr’ythee, tell me what am I?
In a 1999 quiz, the Washington Post asked its readers, “What automobile is referred to in a license plate that reads 1 DIV 0?”
The winning answer came from Supreme Court chief justice William Rehnquist, of all people. What was it?
Montana, Wyoming, and South Dakota meet at one point. Maryland, Virginia, and the District of Columbia meet at two — at Washington’s westernmost and southermost points along the Potomac River.
Name three U.S. states all three of which meet at three different points.
An oldie but a goodie:
From this position, White retracts his last move, then Black retracts his and replaces it with a move that permits White to mate him immediately.
You arrive in purgatory to find it’s just a typewriter on a desk. As you take your seat, you notice that the C key is glowing faintly.
A demon says, “All you have to do is type the integers, in order: ONE, TWO, and so on. The first time you strike the C key, you’ll be released into paradise.”
That doesn’t sound too bad. Assuming it takes 10 seconds on average to type each number (and that you spell each correctly, in English), how much time will pass before you first type the letter C?
You have two one-hour fuses: If you light one, it will be consumed in exactly one hour.
Unfortunately, they’re badly made — some sections of each fuse burn faster than others. You know only that each full fuse will burn in one hour.
Using only these two fuses (and matches to light them), how can you tell when 45 minutes have passed?
From Henry Dudeney:
A ball 13 inches in diameter has a 5-inch hole drilled through the center. How deep is the hole?
At a Cambridge dinner, Arthur C. Clarke asked Clive Sinclair, “What was the first human artifact to break the sound barrier?”
What was it?
John lives in an East Coast state and Mary in a West Coast state. During a phone conversation one night, they realize that it is the same time in both locations. How can this be?
Patented in 1896, Sam Loyd’s “Get Off the Earth” puzzle reportedly sold more than 10 million copies during the puzzlemaker’s lifetime, making it one of the most popular puzzles of all time.
There are 13 men in the figure on the left. Rotating the earth produces the figure on the right — which has 12 men. What happened to the 13th man?
A man drives 1 mile to the top of a hill at 15 mph. How fast must he drive 1 mile down the other side to average 30 mph for the 2-mile trip?
You hate visiting your girlfriend because there’s no elevator in her apartment building. And now she’s moved from the fourth floor to the seventh. How many times longer does this make your ascent?
Many masculine nouns can be converted to feminine with a suffix, as HERO-HEROINE and HOST-HOSTESS.
Name a feminine noun that can be converted to masculine with a suffix.
Every room in my house has an even number of doors.
Prove that the house has an even number of exterior doors.
One train leaves Los Angeles for New York at 60 mph.
At the same time, another train leaves New York for Los Angeles at 40 mph.
What is the distance between them one hour before they meet?
A.A. Bennett offered this puzzle in the American Mathematical Monthly of May 1937:
A car with n (n > 2) passengers of different speeds of mental reaction passes through a tunnel and each passenger acquires unconsciously a smudge of soot upon his forehead. Suppose that each passenger
(1) laughs and continues to laugh as soon as and only so long as he sees a smudge upon the forehead of a fellow passenger;
(2) can see the foreheads of all his fellows;
(3) reasons correctly;
(4) will clean his own forehead when and only when his reasoning forces him to conclude that he has a smudge;
(5) knows that (1), (2), (3), and (4) hold for each of his fellows.
Show that each passenger will eventually wipe his own forehead.
A puzzle by Isaac Asimov:
What word in the English language changes its pronunciation when it is capitalized?
A motorcyclist was sent by the post office to meet a plane at the airport.
The plane landed ahead of schedule, and its mail was taken toward the post office by horse. After half an hour the horseman met the motorcyclist on the road and gave him the mail.
The motorcyclist returned to the post office 20 minutes earlier than he was expected.
How many minutes early did the plane land?