7 Puzzles And Paradoxes To Twist Your Brain

1. The Hat Riddle

What is it?

Finally, we have a riddle that is (a) solvable (b) easy when you know how and (c) tricky enough to impress your friends.

The basic premise is that you and nine others have been captured (probably by aliens) and they are going to eat you unless you can prove that you have the logical skills of a higher-functioning being.

To find this out, they will line you up in height order so that each person can see the people in front of them, but not behind them, and randomly assign each of you a hat that is either black or white. All you have to do is correctly guess the colour of your hat and, if 9 out of the 10 of you get it right, you are all free to go.

You are not allowed to step out of line, look behind you or say anything other than the words "black" or "white".

You are briefly allowed to figure out your strategy with the others whilst the aliens fetch the hats, what do you do?

So what's the solution, wise guy?

The only way you can be sure, is to encode information in the words "black" and "white", in this case, the encoded information should be "odd" or "even".

The person at the back, we'll call them number 1, can see everybody's hats but his own, so rather than guess his hat accurately, he should say "black" for odd and "white" for even. He will communicate to the rest of the group whether he can see an odd or even number of black hats using this system.

For the person in front of him, we'll call them number 2, if they know that the person at the back can see an odd number of black hats, but they can see an even number, then they will know that their hat must be black. If they can also see and odd number of black hats, then they know their must be one of the white ones.

So number 3 will deduce from this (a) the number of black hats and (b) how many of them are behind them and will be able to use this information, along with what they can see in from of them to deduce the colour of their hat.

Make sense? Let us know your thoughts in the comments.

Does science make you tingle in your special place? Like us on Facebook or follow us on Twitter for plenty more.

Want to write for WhatCulture Science? Click here to find out how you could get paid to write about what you love.