# STEM Daily Activity: Tuesday

Throughout this week, we will be running daily competitions: every morning at 10am, we will upload that day’s activity, and anyone who sends in their answer before 9am the following day will be entered into a prize draw, with prizes awarded next week. Solutions to the puzzles will also be uploaded by 10am the following day so you can check your work.

# Tuesday: 4 August

## Cannibals and hats

You are walking through the jungle with 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 person’s 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 know 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?

## Terms & Conditions

1. All students enrolled on the Year 12 Inspire Programme are eligible to enter this competition.
2. You must complete the Competition Cover Sheet and submit it along with your entry to inspire@sjc.ox.ac.uk before the closing date. If we do not receive a completed cover sheet with your entry, we will NOT be able to consider the entry.
3. The competition closes at 9am Wednesday 5 August.
4. The work you submit must be entirely your own, and should not exceed 300 words in length.
5. Competition winners will be contacted via email next week. One entry will be selected at random to win a £10 Amazon voucher and to be published on Inspire Digital.