Today’s puzzles come from Catriona Shearer, a maths teacher at a school in north Essex, whose colourful geometry puzzles have recently gained a following on social media. These brainteasers are certainly pretty, and some are pretty tricky too!

Here are five of her best.

1. Orange segments

If the radius of each semicircle is 5, what’s the total shaded area?

All illustrations © Catriona Shearer

All illustrations © Catriona Shearer

2. Double spiral

Ten equally spaced dots are joined by semicircles to make this spiral. Is more of it shaded red or orange? By how much?


3. Yellow arbelos

The red line, of length 2, is perpendicular to the bases of the three semicircles. What’s the total shaded area?


4. Pink donut

The four dots are equally spaced. What’s the shaded area?


5. Blue triangle

The area of the bottom left square is 5. What’s the area of the blue triangle?


Catriona prefers devising geometry puzzles because – unlike puzzles from other areas of maths – you can often solve them in your head. “I really like puzzles where a bit of clever thinking can sidestep a whole page of algebra,” she says.

“Plus I enjoy colouring them in.”

All these puzzles can be solved with a flash of insight. For some you also need be familiar with the formula for the area of a circle, π x (radius)2, and the Pythagorean theorem, which states that for a right angled triangle the square of the hypotenuse equals the sum of the squares on the other two sides.

I’ll be back at 5pm UK time with the solutions. Meanwhile, thanks to Catriona for the puzzles. If you enjoyed them, follow her on Twitter for many more.

Catriona Shearer

Catriona Shearer

In other two-dimensional geometry news, this tweet about pizza went viral last week. Who said maths was irrelevant to real life?

Fermat’s Library

Here’s a useful counterintuitive fact: one 18 inch pizza has more ‘pizza’ than two 12 inch pizzas

January 7, 2019

I set a puzzle here every two weeks on a Monday. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.


I’m the author of several books of popular maths, and the Football School book series for kids that explains the world through football. The Football School Collection is out now.

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