# Can you solve it? Mirror, mirror on the wall

Hi guzzlers

Here’s a puzzle about something we do every day: gaze at ourselves in the mirror. Who says maths is not relevant to the real world? In fact, You may have often pondered this question without realising it when trying on clothes.

A man is facing a mirror hanging on a wall 1m in front of him.

1. In order for him to see himself entirely in the mirror, what is the minimum possible height of the mirror and where should it be mounted on the wall?
2. He takes a pace backwards so he is 2m from the wall. What is the minimum possible height that the mirror now needs to be so he can see himself completely? Is the mirror larger or smaller than the one before?

(The puzzle requires some basic physics, which I will spell out here. First, light travels in a straight line. Secondly, when light reflects in a mirror the angle of incidence is equal to the angle of reflection. In other words, light hitting a mirror behaves just like a snooker ball bouncing against the side cushion: the angle it hits the cushion is the same as the angle of the rebound.)

I’ll be back at 5pm with the solution. Meanwhile, NO SPOILERS!!!

UPDATE: The solution to the puzzle can be read here.

Before I go, here’s my latest video for Football School, a book series I write with Ben Lyttleton aimed at 8-12 year-olds that uses football as a way to explore the world. Please share with all young footie fans!

Thanks to Spanish magician Carlos Vinuesa for telling me about the mirror puzzle.

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, including the puzzle books Can You Solve My Problems? and Puzzle Ninja. I also co-write the children’s book series Football School.

Alex Bellos

The Guardian

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