How many pets do I have if all of them are dogs except two, all are cats except two, and all are fish except two?

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“Four Puzzles in One”


By Sam Loyd. Place the black king (a) where it can be checkmated on the move, (b) where it’s in stalemate, (c) where it’s in checkmate, and (d) where the three white pieces can’t be arranged to checkmate it.

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Mate in Two


By G.A.A. Walker. White to play and checkmate all six black kings simultaneously with his second move.

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A Mysterious Windfall

A riddle by Isaac Newton:

Four people sat down at a table to play;
They play’d all that night, and some part of next day;
This one thing observ’d, that when all were seated,
Nobody play’d with them, and nobody betted;
Yet, when they got up, each was winner a guinea;
Who tells me this riddle I’m sure is no ninny.

Who are the players?

Erin Go

Count these leprechauns:

vanishing leprechaun 1

Now swap the two upper panels and count again:

vanishing leprechaun 2

Where has the extra one been hiding?

Hidden in Sight

This puzzling verse, from a contributor named “Maude,” appeared in the Weekly Wisconsin of Sept. 29, 1888:

Perhaps the solvers are inclined to hiss,
Curling their nose up at a con like this.
Like some much abler posers I would try
A rare, uncommon puzzle to supply.
A curious acrostic here you see
Rough hewn and inartistic tho’ it be;
Still it is well to have it understood,
I could not make it plainer, if I would.

(In the second line, “con” means “contribution.”)

What are the concealed words?

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

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“White to mate in half a move.”

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A Curious Exchange

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?

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The Canals on Mars


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.

Equal Time


Image: Flickr

A puzzle from Russia:

Draw two straight lines on the clock face so that the sums of the numbers in each part are equal.

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Arms Race

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?

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Claws and Effect

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?

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What Am I?


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?

Escape From Elephantistan

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?

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What Am I?

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?

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Car Code

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?

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Map Twist

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.

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retractor chess problem

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.

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C Story

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?

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Burning Time

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?

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dudeney drilled ball puzzle

From Henry Dudeney:

A ball 13 inches in diameter has a 5-inch hole drilled through the center. How deep is the hole?

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A Riddle

At a Cambridge dinner, Arthur C. Clarke asked Clive Sinclair, “What was the first human artifact to break the sound barrier?”

What was it?

Fugue State


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?

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A Vanishing

get off the earth

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?