Can you solve it? A tray of Portuguese delights | Mathematics

Today, four tasty treats from Paulo Ferro, a puzzlesmith from Porto.

1. Trapezium or trap-not-so-easy-um?


The trapezium is composed of 7 matchsticks. Move the positions of 3 matchsticks in order to obtain 2 equilateral triangles.

(The final arrangement must use all the matchsticks, and have no extraneous lines.)

2. Nine times table


The number 403 is created out of 15 matchsticks. Move the positions of two matchsticks to obtain a number divisible by 9.

For example, two from the first digit moved to the third digit give you 108. Find the other four solutions.

3. Touching squares


Two squares meet at the centre of a circle. The light blue square has area 20.

What is the area of the dark blue square?

4. Pent-up thoughts


A regular pentagon and a square have the same side length.

What is the size of the angle?

(For these two geometrical puzzles, you will need to know Pythagoras’s Theorem, which states that for right-angled triangles, the square of the hypotenuse is equal to the sum of the squares on the other two sides. You will also need to be aware that the internal angles of a triangle, a quadrilateral and a pentagon add up to 180, 360 and 540 degrees respectively.)

Paulo is a maths educator from Porto, whose brilliant EnigMaths website is packed with resources. He has also written his first book of geometry puzzles, Birds, Bees and Burgers, which is out now. (And which includes puzzle 4 above.)

I’ll be back with the solutions at 5pm UK time today. PLEASE NO SPOILERS. Instead discuss Portuguese patisserie. Obrigado!

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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 puzzles, most recently the Language Lover’s Puzzle Book.

You can follow Paulo Ferro on Twitter.


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