Another Christmas Quiz

This year’s GCHQ Christmas Challenge is now live. Devised by Government Communications Headquarters, the British intelligence agency, this year’s quiz presents seven puzzles for children aged 11-18. They’re designed to test a range of problem-solving skills, including creativity and intuitive reasoning.

Agency director Anne Keast-Butler said: “Puzzles are at the heart of GCHQ’s work to keep the country safe from hostile states, terrorists and criminals; challenging our teams to think creatively and analytically every day.”

December 11, 2025December 10, 2025 | Puzzles

Dividing Line

Draw a circle and choose 100,000 points at random in its interior. Is it always possible to draw a line through the circle such that 50,000 points lie on each side of it?

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Yes. Draw a line ℓ that doesn’t intersect the circle, and choose a point P on it that doesn’t lie on any of the lines determined by pairs of points within the circle. Rotate ℓ about P. It will pass through all the points in the circle one at a time (because it can’t encounter two at once). Stop when it’s passed 50,000 points. From Claudi Alsina, Charming Proofs, 2010.

December 10, 2025December 10, 2025 | Puzzles

Tableau

In Arthur Ransome’s 1933 children’s novel Winter Holiday, Nancy Blackett, quarantined with mumps, sends a picture to her friends of a sledge being drawn by skating figures. Nancy is encouraging the group to pursue their plan to explore a frozen lake. The seven figures in the picture correspond to the seven children in the group. “But,” asks Peggy, “what did she put in the crowd for?”

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It’s a message in semaphore. The children had earlier discussed the semaphore alphabet; reading right to left, the figures in the picture are spelling out WHO IS SLEEPING IN THE FRAM?, a houseboat named for Fridtjof Nansen’s Arctic exploration vessel. Nancy was proposing that one of the children spend the freezing nights in the warmth of the ship’s stove. Sherlock Holmes solves a similar cipher in Arthur Conan Doyle’s 1905 story “The Adventure of the Dancing Men.”

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December 9, 2025December 8, 2025 | Puzzles

Saving Santa

Mathematician Matthew Scroggs’ 2025 advent calendar offers 24 puzzles, each of which has a three-digit answer. The answers will help you order the parts that Santa needs to rebuild his sleigh and save Christmas.

A new puzzle is revealed each day. Prizes will be awarded to 10 entrants who successfully build a sleigh before the end of the year. Details are here.

December 8, 2025December 7, 2025 | Puzzles

Progress

In 2012 I mentioned that Helen Fouché Gaines’ 1956 textbook Cryptanalysis: A Study of Ciphers and Their Solution ends with a cipher that’s never been solved. Reader Michel Esteban writes:

I think I found what kind of cipher Helen Fouché Gaines’ last challenge is.
In my opinion, it is a seriated Playfair of period 5 with two peculiarities:
– Zs are nulls in the ciphertext,
– Z is the omitted letter in the cipher square (instead of J).
If I am right, period 5 is the most likely reasonable period: we can observe no coincidences between upper and lower letters.
On the other hand, six reciprocal digrams appear: FD-DF, EC-CE, JN-NJ, JB-BJ, QL-LQ and GW-WG. These are almost certainly cipher counterparts of common reciprocal digrams (ES-SE, EN-NE, IT-TI, etc.).
I did not solve this cipher, because it is too short to use statistics. The only way to solve it is to use some metaheuristics (like Hill Climbing), but I have no computer!
I have no doubt you know someone that will be able to unveil the plaintext after having read these considerations.

Can someone help? I’ll add any updates here.

December 5, 2025December 4, 2025 | Puzzles · Science & Math

The Roving Wazir

A wazir is a fanciful chess piece that can move one square horizontally or vertically, but not diagonally. This one finds itself in the upper left corner of the board. Can it make its way to the lower right while visiting each square exactly once?

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No. The nature of the wazir’s move means that it visits light and dark squares alternately. The board has 64 squares, and the piece begins on a light square, so a successful journey would end on a dark one. The target square is light, so the task is impossible. Simple enough!

December 3, 2025December 2, 2025 | Puzzles

Query

From Gerald Lynton Kaufman’s The Book of Modern Puzzles (1954):

All DROONS are the same size and shape.
All green SLACKENS are the same size and shape.
Twenty DROONS just fill up a MULDRUFF.
All WALLAXES contain green SLACKENS.
A green SLACKEN is 10% bigger than a DROON.
A WALLAX is smaller than a MULDRUFF.

“If all MULDRUFFS and all WALLAXES are predominantly RED throughout, what is the largest possible number of green SLACKENS in a WALLAX?”

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Eight. If a MULDRUFF holds 20 DROONS, and a green SLACKEN is 10% bigger than a DROON, then a MULDRUFF can accommodate at most 18 green SLACKENS. And if a WALLAX is smaller than this, then it can hold at most 17 green SLACKENS. But if each WALLAX is predominantly red, then the proportion of green SLACKENS in its contents can’t be more than one-half. So the largest number of green SLACKENS it can contain is 8. 11/22/2025 UPDATE: This is just wrong. Let a DROON have size 1. Then a MULDRUFF has capacity 20, and a green SLACKEN has size 1.1. So our MULDRUFF will accommodate 9 green SLACKENs (= 9.9) and 10 DROONS (= 19.9 < 20). Now we can transfer this cargo to a WALLAX of, say, capacity 19.95 and fulfill the terms of the problem with 9 (not 8) green SLACKENS — the WALLAX remains predominantly red by both number and volume. Thanks to everyone who wrote in about this.

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November 20, 2025December 13, 2025 | Puzzles

Constitution

A sobering problem from Gerald Lynton Kaufman’s Book of Modern Puzzles, 1954:

If a GLEEPER is as long as two PLONTHS and a half-GLEEPER, and a BLAHMIE is as long as two GLEEPERS and a half-BLAHMIE, and a POOSTER is as long as two BLAHMIES and a half-POOSTER, then how many PLONTHS long is a half-POOSTER?

“It may help you to make a sketch.”

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Four PLONTHS make a GLEEPER, four GLEEPERS make a BLAHMIE, and four BLAHMIES make a POOSTER. So half a POOSTER is 32 PLONTHS.

November 10, 2025November 9, 2025 | Puzzles

Black and White

brotherton chess problem

With this problem D.W.A. Brotherton won second prize in a 1955 competition for British composers under 21. White to mate in two moves.

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1. Rf5! 1. … Kh7+ 2. Rf8# 1. … Rh7 2. Rb8# 1. … g6/5 2. Bc4# 1. … B any 2. Rxg7# From The Problemist.

November 6, 2025November 5, 2025 | Puzzles

Character Study

A puzzle by Paul Hoffman, from Science Digest. Could this game ever have resulted from a strict adherence to the rules of tic-tac-toe (noughts and crosses)?

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No. The player with the Xs has won and so must have made the last move. If that player moved first, then there ought to be one more X than there are Os in the diagram. If the player making Os went first, then there should be an equal number of Os and Xs. The diagram contains more Os than Xs, so the position is impossible. From Dr. Crypton and His Problems: Mind Benders From Science Digest, 1982.

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November 3, 2025November 2, 2025 | Puzzles