GCHQ Christmas Challenge 2023 solution
The UK’s Government Communications Headquarters (GCHQ) publishes an annual Christmas Challenge, which takes the form of a Christmas card from its director to other intelligence agencies.
This page gives the solutions to the Christmas Challenge 2023, which was published this morning, 14th December 2023.
Question 1: TIME
In 24-hour format, the times displayed by the clocks are 20:00, 9:00, 13:00, and 5:00. Converting the hours to letters (by treating 1 as A, 2 as B, and so on) gives the word TIME.
Question 2: DAY
This is a riddle. A DAY can break (at dawn), leap (on February 29th), be seized (the Latin phrase carpe diem is translated as seize the day), and be present (today is the present day).
Question 3: PUDDING
The three groups are:
- Declan, Jasmine, and Sticky, which can be followed by Rice (Declan Rice is a footballer and jasmine rice and sticky rice are food)
- Beverly, Pudsey, and Scarborough, which are towns in Yorkshire
- Penny, Pitch, and Sirius, which can be followed by Black (a Penny Black is a stamp, pitch black means completely dark, and Sirius Black is a fictional character)
The three words Rice, Yorkshire, and Black can be followed by pudding to give three foods.
Question 4: TREE
This is a common form of puzzle where each letter represents a distinct digit.
The only solution to MI × MI = MAA with distinct digits is 12 × 12 = 144.
For TI + TI = RA, R must be double T (as we already know I is 2 so there isn’t a carry into the tens), and with 1, 2, and 4 already used the only solution is 32 + 32 = 64.
In DO - SO + TI - MI = RE, the Os and Is cancel out, so E is 0. We don’t need to know what the other letters represent solve the rest of the question, but the solution is 98 - 58 + 32 - 12 = 60.
Finally RE × RE is 60 × 60, which is 3600. This is equivalent to TREE.
Question 5: STOCKING
The four sequences seem to be connected to doing things backwards (if wrapping is treated as the backwards version of unwrapping):
- The first sequence is TH RD ND ST, which are the letters in the ordinals counting down from 4 (4th, 3rd, 2nd, and 1st)
- The second sequence is ET EL PM OC: the word complete backwards
- The third sequence is WU SQ OM KI: the letters go backwards through the alphabet in steps of two.
- The fourth sequence is WR AP PI NG: the word wrapping
The final letters of each sequence spell STOCKING.
Question 6: CAROL
Each set of five notes is treated as a binary number, with a minim (with an unfilled circle) representing 0 and a crotchet (with a filled circle) representing 1. This gives the numbers 3, 1, 18, 15, and 12. Converting these to letters (by treating 1 as A, 2 as B, and so on) gives the word CAROL.
Question 7: FILM
This is a basic form of encryption called a monoalphabetic substitution cypher, where each letter corresponds to another letter. The usual approach to solving this form of encryption is to look at the frequencies of each letter, but this message seems to have been designed to make this difficult, by infrequently using common letters such as A and frequently using rare letters such a V.
However, by guessing that C 4-HMQQMK VDKE is equivalent to A 4-LETTER WORD, the rest of the message is easy to decrypt:
First solve the code
Identify a 4-letter word
Look everywhere
Maybe it’s very obvious
The first letter from each of the four lines gives the word FILM.
Final challenge: YULETIDE FELICITATIONS
To solve the final message, note that each pattern occurs on a specific item in the picture on the front of the card, and that these items are also shown behind the question numbers. Taking the appropriate letter from each question’s solution as specified by the number next to the pattern gives the solution to the final challenge, YULETIDE FELICITATIONS.