One of Eduard Gufeld’s first chess coaches, A.A. Olshansky, offered him this problem:

“White to mate in half a move.”

Census Taker: How old are your three daughters?

Mrs. Smith: The product of their ages is 36, and the sum of their ages is the address on our door here.

Census Taker: (after some figuring) I’m afraid I can’t determine their ages from that …

Mrs. Smith: My eldest daughter has red hair.

Census Taker: Oh, thanks, now I know.

How old are the three girls?

From Sam Loyd:

Here is a map of the newly discovered cities and waterways on our nearest neighbor planet, Mars. Start at the city marked T, at the south pole, and see if you can spell a complete English sentence by making a tour of all the cities, visiting each city only once, and returning to the starting point.

When this puzzle originally appeared in a magazine, more than fifty thousand readers reported, ‘There is no possible way.’ Yet it is a very simple puzzle.

I’ll withhold the answer.

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:

1. No kitten that loves fish is unteachable.
2. No kitten without a tail will play with a gorilla.
3. Kittens with whiskers always love fish.
4. No teachable kitten has green eyes.
5. 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?