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.

Screen Shot 2018-09-19 at 13.25.56

  • 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!

Science Oxford Interview: From Togas to Tattoos…

I was interviewed by Autumn Neagle at Science Oxford about my toga-clad exploits in FameLab and the meaning of my maths-based tattoos… You can read the full article here.

What did you enjoy most about the FameLab experience?

“I’d been aware of FameLab for a few years, but I’d never entered because I thought that you had to talk about your own research – and with mine being lab-based I didn’t think it would translate very well to the live element of the show. But, once I found out that I could talk about anything within the subject of maths then it was a whole different ball game and I just had to give it a go. I think my favourite part was actually coming up with the talks themselves, just sitting down and brainstorming the ideas was such a fun process.”

What did you learn about yourself?

“The main takeaway for me was the importance of keeping to time. I knew beforehand that I was not the best at ‘following the rules’ and I think that both of my FameLab talks really demonstrated that as I never actually managed to get to the end of my talk! This was despite practicing several times beforehand and coming in sometimes up to 30 seconds short of the 3-minute limit – I think once I’m on stage I get carried away and just don’t want to come off!”

What about post-FameLab – how has taking part made a difference?

“Well, I certainly now appreciate the comfort and flexibility of wearing a toga that’s for sure! But on a more serious note, I think the experience of being on stage in front of a live audience really is invaluable when it comes to ‘performing maths’ – and I say ‘performing’ because that’s now how I see it. Before I would be giving a lecture or a talk about maths, but now it’s a full-on choreographed performance, and I think taking part in FameLab really helped me to understand that.

Any tips for future contestants?

“It has to be the time thing doesn’t it! I think everyone knows to practice beforehand to ensure they can get all of the material across in the 3-minutes, but for me that wasn’t enough. I’d suggest doing the actual performance in front of a group of friends or colleagues because – if they’re anything like me – then the adrenaline rush of being on stage changes even the best rehearsed routines and you can only get that from the live audience experience.”

What are you up to now/next?

“I’ve actually just received an award from the University of Oxford for my outreach work which is of course fantastic but also completely unexpected! I really do just love talking to people about maths and getting everyone to love it as much as I do, so the plan is very much to keep Tom Rocks Maths going and to hopefully expand into television… I have a few things in the pipeline so watch this space.”

Are all of your tattoos science inspired and if so what’s next?

“Now that I’ve reached the dizzy heights of 32 tattoos I can’t say that they are all based on science or maths, but it’s definitely still one of the dominant themes. So far I’ve got my favourite equation – Navier-Stokes, my favourite shapes – the Platonic Solids, and my favourite number – e. Next, I’m thinking of something related to the Normal Distribution – it’s such a powerful tool and the symmetry of the equation and the graph is beautiful – but I’ve yet to figure out exactly what that’s going to look like. If anyone has any suggestions though do let me know! @tomrocksmaths on social media – perhaps we can even turn it into a competition: pick Tom’s next tattoo, what do you think?”

In your YouTube video’s #EquationsStripped you reveal the maths behind some of the most important equations in maths, and I noticed that you describe the Navier-Stokes equations as your favourite – why is that and perhaps most importantly can you solve them?

“My favourite equations are the Navier-Stokes equations, which model the flow of every fluid on Earth… Can I solve them? Not a chance! They’re incredibly complicated, which is exactly why they’re a Millennium Problem with a million-dollar prize, and my idea with the video and live talk is to try to peel back the layers of complexity and explain what’s going on in as simple terms as possible.”

Does that mean that anyone can follow your video?

“The early parts yes absolutely, I purposefully start with the easier bits – the history, the applications, and then gradually get more involved with the physical setup of the problem and finally of course the maths of it all… And that’s pretty much where the idea to ‘strip back’ the equations came from – I thought to myself let’s begin simple and then slowly increase the difficulty until the equation is completely exposed. Being the ‘Naked Mathematician’ the next move was pretty obvious… as each layer of the equation is stripped back, I’m also stripping myself back until I’m just in my underwear – so almost completely exposed but not quite!”

Where did the whole idea of ‘stripping’ equations come from?

“I suppose I don’t really see it as ‘stripping’ per se, it’s there for comedic effect and really to show that maths is not the serious, boring, straight-laced subject that unfortunately most people think it is. Stripping for the videos is fine – it’s just me alone with my camera, but then earlier this year I was asked to give a live talk for the Oxford Invariants Society and they were very keen to emphasise that they wanted to see the Naked Mathematician in the flesh – quite literally!”

And how did it go?

“Well, barring some slightly awkward ‘costume changes’ between the layers of the equation – I went outside for the final reveal down to my underwear for example – it was good fun and definitely something I’d be keen to try out again… Perhaps maybe even an Equations Stripped Roadshow. I’m keen to try out anything that helps to improve the image that people have of maths.”

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.

tragic-deaths

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.

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