Time for the next puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Facebook, Twitter, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.
You are out walking two friends when all of a sudden you are attacked by a group of cannibals. Fortunately, they do not eat you straightaway, but instead devise a puzzle that you must solve to avoid being eaten. The setup is as follows:
- You are each tied to a pole such that you can only see forwards. The poles are placed in a line such that the person at the back can see the two people in front of them, the person in the middle can see one person in front of them, and the person at the front cannot see anyone else. See diagram below.
- The cannibals produce five hats: 3 are black and 2 are white. You are all then blindfolded and a hat is placed on each persons head at random. The other two hats are hidden.
- The blindfolds are removed and you are told that you will be set free provided that one of the group can correctly guess the colour of the hat that they are wearing. An incorrect guess will cause you all to be eaten.
- The person at the back says that they do not know the colour of their hat. The person in the middle says that they also do not now the colour of their hat. Finally, the person at the front says that they DO know the colour of their hat.
The questions is: what colour hat is the person at the front wearing and how did they know the answer?
The answer will be posted in a few weeks along with the next puzzle – good luck!
The person at the front wears a black hat.
1. If the person at the back does not know the colour of their hat, it means that at least one of the persons in front must wear a black hat, because if both were white, he would know for sure that their hat is black (given that there are only two white hats).
2. If the person in the middle does not know their hat, it means that the person in front is wearing a black hat, because if it were white, he would know for sure that their hat is black (since either the person at the front or in the middle have to wear a black hat).
3. Thus the person at the front can conclude that their hat is definitely black.