Turnabout

triangle reversal puzzle

A puzzle by A. Khalamaizer: Move three of these circles to make the triangle point downward.

	Select Click for Answer
From the July-August 1996 issue of Quantum. Similar: Wildlife Management and Horse Sense.

September 25, 2026September 24, 2026 | Puzzles

Black and White

expedient chess puzzle 1

I don’t know who devised this; I found it in The Batsford Chess Puzzle Book (2002). Black has only a king and a bishop, while White still has all 16 of his men. But Black threatens to take White’s knight, giving mate immediately. If each side uses every legal expedient, what will be the outcome? For a start, White can stave off mate with 1. Bh2!

	Select Click for Answer
1. Bh2 Bxh2 2. g3 Bxg3 3. Rf4 Bxf4 4. d6 Bxd6 5. Qh2! Bxh2 6. Re5 Bxe5 7. Nb5 Bf4 8. f6 (the only legal alternative to moving the needed b5 knight) Bxc7 9. Nxc7 and the game is drawn by stalemate!

September 24, 2026September 28, 2026 | Puzzles

Pardon?

What word has kst in the middle, and at the end, and in at the beginning?

	Select Click for Answer
Inkstand.

September 23, 2026September 22, 2026 | Puzzles

Dead Man’s Chest

Five pirates of different ages want to divide a treasure of 100 gold coins. They agree that the oldest among them will propose how to divide the coins, and then all the pirates will vote on the proposal. If more than half the pirates support it, it will be adopted and the coins distributed accordingly. Otherwise the proposer will be thrown overboard and the process repeated with the remaining pirates.

If all five pirates are smart, rational, greedy, and fearful of death, what will happen?

	Select Click for Answer
Work backward: If there are only two pirates, the elder will need to give all 100 coins to the younger or he’ll go to the sharks. If there’s an intermediate pirate, though, the eldest can pay him 1 coin to gain his cooperation. The youngest, outvoted, must then accept nothing. So, youngest to oldest, the three would receive 0, 1, and 99 gold pieces. If there are four pirates, the division is 1, 2, 0, 97. The two youngest pirates must be bribed just enough to oppose throwing the proposer overboard and arriving at the three-pirate disposition immediately above. Similarly, with five pirates the eldest should propose the division 2, 0, 1, 0, 97, youngest to oldest. By spending just 3 coins judiciously, the eldest pirate can get the majority he needs. From the Wikibooks puzzle collection. Somewhat related: How can three people divide a cake amenably?

Click for Answer

September 21, 2026 | Puzzles

Spin Doctor

I have 13 magnetic tapes on reels; one empty reel; and a machine that can unwind a tape from a full reel onto an empty one, reversing the tape’s direction. I need to reverse the direction of each tape while leaving it on its original reel. Can this be done?

	Select Click for Answer
No. If each of the 13 reels must end with the tape it started with, then each of these reels must go through an even number of tape transfers. The empty reel, too, must go through an even number of transfers to remain empty. But each of the 13 tapes must be wound or rewound an odd number of times to end up reversed. These facts can’t be reconciled, so the task can’t be done. From Dick Hess’ excellent All-Star Mathlete Puzzles, 2009.

Click for Answer

September 18, 2026 | Puzzles

Kakuro

This logic puzzle is the numerical equivalent of a crossword. Each white cell in the diagram is to be filled with a digit from the range 1-9. The sum of each string of digits must match the “clue” given in the diagram. For example, the clue 29 above means that the four digits to its right must sum to that total. No digit may be duplicated within any entry. Can you complete the diagram?

	Select Click for Answer
Image: Wikimedia Commons

September 12, 2026September 11, 2026 | Puzzles

Self-Study

A puzzle from the October 1962 issue of Eureka, the journal of the Cambridge University Mathematical Society:

(a) At least two of these statements, apart from this one, are true.
(b) At least two of these statements, apart from this one, are false.
(c) At least one of these statements is false.
(d) x of these statements are true.

Given that, if you knew the value of x, you could determine uniquely which statements are true and which are false, determine the value of x.

	Select Click for Answer
The journal states only that x = 3, but here’s an attempt. We’re told that the value of x in (d) is vital, so (d) must be true; otherwise its claim about x would be useless. It’s impossible for all four statements to be true, because then (a) and (b) would contradict one another. This means that at least one statement is false, which means that (c) is true. And if (c) and (d) are both true, then (a) is true, which means that (b) is false: (a) true (b) false (c) true (d) true

Click for Answer

September 11, 2026 | Puzzles

Orb Weaver

An elegant alphametic by Jonathan Joseph, from the October 1991 issue of Games magazine:

   VENUS
    MARS
  SATURN
+ URANUS
--------
 NEPTUNE

If each letter consistently represents a particular digit, what equation does this expression encipher?

	Select Click for Answer
20163 4593 358691 + 695163 -------- 1078610

September 8, 2026September 7, 2026 | Puzzles

Flight From Moscow

Russian chess master Alexander Petrov composed this puzzle to commemorate Napoleon’s defeat in 1812:

petrov chess puzzle

Currently the emperor stands in Moscow, on h7. The goal is to chase him all the way back to Paris and to checkmate him there. The white knights are Cossack cavalry, and the white bishops are Russian partisans. Given these clues, which square represents Paris?

	Select Click for Answer
Paris is a3. The white knights will check from g5, h6, h7, g8, f8, e7, d7, c8, b8, a7, a6, and b5. All of Black’s replies are forced. Via the Batsford Chess Puzzle Book, 2002.

September 2, 2026September 1, 2026 | History · Puzzles

For Short

In 2007 I posted this cryptic verse by William Whewell:

U 0 a 0 but I 0 U,
O 0 no 0 but O 0 me;
O let not my 0 a 0 go,
But give 0 0 I 0 U so.

You sigh for a cipher but I sigh for you,
O sigh for no cipher, but O sigh for me;
O let not my sigh for a cipher go,
But give sigh for sigh, for I sigh for you so.

In An Almanac of Words at Play (1975), Willard R. Espy offered this addition. What does it say?

Oy OO thO he O
2 On an OO. OO bO
An OO but he never thO
He’d O the OO dealer O
For the OO OO bO.
Say, has OO’s OO brO
OO O that OO sO?
OO’s OO’s good for nO.

	Select Click for Answer
Naughty Otto thought he ought To own an auto. Otto bought An auto but he never thought He’d owe the auto dealer aught For the auto Otto bought. Say, has Otto’s auto brought Otto aught that Otto sought? Otto’s auto’s good for naught.

August 29, 2026August 28, 2026 | Language · Puzzles