The final episode in season 1 of Tom Rocks Maths on Oxide Radio – Oxford University’s student radio station – with very special guests Jon and Nick discussing everything from the number of stickers needed to cover the Earth, to different types of infinity, via a new name for the world’s smallest number. Plus, a mammoth quiz to end the season in style and music from Nirvana and Soundgarden. This is maths, but not as you know it…

# Cannibals and hats

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 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 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!

# Crossing the desert

The fifth puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Twitter, Facebook, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

You are responsible for driving an important person across the desert, but the cars that you have been given can only hold enough petrol to cover half of the distance. Being a desert, there are of course no petrol stations along the way. However, you have access to as many cars as you need and can transfer petrol between them.

**What is the minimum number of cars that you will need and how can you complete the journey?**

WARNING: answer below so scroll slowly to avoid revealing it accidentally.

**ANSWER**

The minimum number of cars required is 4. The journey can be split up as follows.

- All four cars travel 1/4 of the distance across the desert, each using up one half of a tank.
- Two of the cars are then emptied leaving two cars remaining, each with a full tank.
- The two cars travel a further 1/4 of the distance, reaching half-way across the desert, each with one half of a tank remaining.
- One car is then emptied, leaving one car remaining with a full tank.
- The final car drives the remaining half of the distance across the desert using the full tank.

**BONUS**

How many cars do you need if a full tank of petrol allows each car to travel 1/3 of the distance across the desert? What about if a full tank only reaches 1/4 of the way across? Finally, what is the general rule for the number of cars needed to cross the desert when a full tank of petrol takes you 1/n of the total distance?

# Thick and sticky fluids

The fourth puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Twitter, Facebook, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

Viscosity is a property of a fluid on the molecular scale and is a measure of the strength of the internal friction between fluid particles. What this means in practice is that the thicker and stickier the fluid, the higher its viscosity.

Your task in this week’s puzzle is to order the six fluids below by their viscosity, lowest first. The answer will be posted in 2 weeks along with the next puzzle – good luck!

**WARNING:** answer below image so scroll slowly to avoid revealing it accidentally.

**ANSWER**

3. Air 1.81 x 10^{-5} [Pa s]

2. Water 8.9 x 10^{-4}

1. Blood 3 x 10^{-3 }

6. Honey 2-10 [Pa s]

5. Ketchup 50-100 [Pa s]

4. Peanut butter 250 [Pa s]

# A mathematicians age is but a number…

The third puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to @tomrocksmaths on Twitter, Facebook, Instagram or via the contact form on my website. The answer to the last puzzle can be found here.

Can you place the (extremely) famous mathematicians below in order of the year that they were born, earliest first? Bonus points for telling me what they studied.

WARNING: answer below image so scroll slowly to avoid revealing it accidentally.

b. Fermat: 1601-1665 – The French mathematician behind the infamous ‘Last Theorem’ written in the margins of his copy of *Arithmetica *in 1637. The theorem was finally shown to be true by Andrew Wiles 358 years later.

d. Newton: 1643-1727 – Most famous for his formulation of the Law of Gravity, but he also made significant contributions to geometry and is credited with developing calculus alongside Leibniz.

a. Euler: 1707-1783 – He worked on every almost every area of maths, but perhaps most famous for Euler’s number e=2.718… and Euler’s identity e ^{iπ} + 1 = 0.

c. Gauss: 1777-1855 – Like Euler, Gauss worked across all branches of maths and made significant contributions to Statistics with the Gaussian Distribution and physics with Gauss’ Flux Law.

# The Tragic History of Mathematicians

The second puzzle in the new feature from Tom Rocks Maths – check out the question below and send your answers to me @tomrocksmaths on Twitter, Facebook, Instagram or via the contact form on my website. The answer to the first puzzle can be found here.

Below are portraits of four famous mathematicians from history that have all died in tragic circumstances. Your task is to match up the mathematician with one of the following causes of death:

- Shot in a duel
- Pushed overboard from a ship
- Suicide
- Lost his mind

Bonus points for explaining the work of any of the mathematicians shown. Good luck!

WARNING: answer below image so scroll slowly to avoid revealing it accidentally.

Answer:

a. Hippasus – Pushed overboard from a ship for his discovery and subsequent proof that the square root of 2 is an irrational number (cannot be written as a fraction).

b. Cantor – Lost his mind after discovering that there are more one type of infinity. For example the positive integers (whole numbers) are countably infinite, whilst the real numbers are uncountably infinite.

c. Boltzmann – Suicide. He is most famous for the development of statistical mechanics which explains how the properties of atoms determine the physical properties of matter.

d. Galois – Shot in a duel after being involved in a ‘love triangle’. Fortunately he wrote down all of his work/thoughts the night before which now forms the basis of Galois theory.

# Funbers 9

We love the number 9 as humans – perhaps due to the 9 months we spend inside our mother’s womb before birth… There are also LOADS of fun maths tricks that you can do with the last single-digit number, with my two favourites explained in the video below.

You can listen to all of the Funbers episodes from BBC Radio Cambridgeshire and BBC Radio Oxford here.