Christmas puzzles

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It’s Christmas Eve. By Boxing Day, you will probably be looking for something to do between mouthfuls of leftover turkey. If so then you’re in the right place: this blog post is full of Christmassy puzzles for you to spend your time on! advent calendar

This year, the front page of has an advent calendar full of puzzles. Here are a few of the best puzzles:

5 December

How many different triangles are there with a perimeter of 100 and each side having an integer length?

(different = not rotations or reflections)

9 December

You start at A and are allowed to move either to the right or upwards.


How many different routes are there to get from A to B?

12 December

Put the digits 1 to 9 (using each digit exactly once) in the boxes so that the sums reading across and down are correct. The sums should be read left to right and top to bottom ignoring the usual order of operations. For example, 4+3×2 is 14, not 10.


The answer is the product of the digits in the red boxes.

There are prizes available for solving all the puzzles. Head over to and enter your answers!

GCHQ’s Christmas puzzles

If the advent calendar puzzles are too easy for you, then you should try the director of GCHQ’s Christmas puzzles.

These puzzles begin here with this:

Click for a larger version.

Click for a larger version.

In this puzzle, the numbers tell you which blocks of black appear in the rows and columns. For example, the clue “1 1 3” tells you that there is a block of black one square long followed by another one square long, followed by a block three squares long (although, the space between the blocks can be of any size).

The solution of this puzzle is a QR code which directs you to the page containing the second round of puzzles. In total, there are five rounds of puzzles, each harder than the last. Here are a few choice selections from the first three rounds:

Round 2 Question 2

What comes after GREEN, RED, BROWN, RED, BLUE, -, YELLOW, PINK?

Round 3 Question B

$$\text{pest} + \sqrt{\text{unfixed} – \text{riots}} = \text{?}$$

If you can complete all five rounds before the end of January, then you can submit your answers and a winner will be selected. If you enjoy these puzzles, it is suggested that you make a donation to the National Society for the Prevention of Cruelty to Children.

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Matthew Scroggs is a PhD student at UCL working on finite and boundary element methods. His website,, is full of maths and now features a video of him completing a level of Pac-Man optimally.
Twitter  @mscroggs    Website    + More articles by Matthew

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