Visiting Speaker: Zoe Griffiths

 On Tuesday, 10th June, the brilliant mathematician, Zoe Griffiths, came to St. Paul’s to give some 5th form students a fun and interactive presentation about ‘Mathematics of the Unexpected’.

Having entered the John Colet Hall, we sat down at desks in pairs and were immediately greeted by a jovial and comical Zoe. Not only has she appeared on the YouTube Channel Numberphile, but she has also been on BBC Radio 4, performing mathematical comedy sets. Needless to say, she gave off a lot of positive energy, which made us all very excited about the two hours ahead of us.

We began by investigating the secrets of some magic tricks, such as the seemingly mind-boggling fact that any 3-digit number repeated after itself (e.g. 738738), when divided by 7, will always produce a whole number. Surely, we would expect only a seventh of the numbers to be a multiple of 7? In fact, this new number divides by 13, 11 and 7. Now, 13 x 11 x 7 =1001 and 1001 multiplied by any 3-digit number produces a number that repeats the 3 digits.

For example,                      

                                    738 x 1001 = 738738

                                    265 x 1001 = 265265

A very clever James B managed to work out this trick just ahead of the rest of us.

Eager for more magic to impress our friends with, we carefully paid attention to the next trick. This one revolved around base-3, or ternary. For context, we usually use base-10, or decimal. A card trick was performed, whereby the ordering of certain piles led to Zoe finding a random card among 27, which is 3³. After a bit of careful thinking, we deduced how the arrangement of cards influences the position of the random card, making it possible to find after three sets of shuffles. Here is a video of the full explanation by Matt Parker: https://youtu.be/l7lP9y7Bb5g

 My personal favourite section was a game that involved dice. Given three dice with differently numbered faces, we had to work out which would be the best to roll if competing against a friend with the same choice as us.

The faces were as follows:

A comparison matrix was used to show that, interestingly, there is no real best choice, because Red beats Blue, Blue beats Olive, and Olive beats Red!

These are known as non-transitive dice.

This is similar to rock, paper, scissors.

However, it becomes even more interesting when we find that if two dice of the same colour are rolled together in competition with another dice pair, the chain reverses!

Here is a link to an article that explains non-transitive dice in more detail and will introduce you to other interesting sets of dice. https://www.singingbanana.com/dice/article.htm

Overall, I found the afternoon very interesting and enjoyable, and I am sure everyone there had fun and learnt something new, whether it be how to count in ternary, or that 8208 is a Narcissistic Number (8⁴ + 2⁴ + 0⁴ + 8⁴ = 8208 where the power is the number of digits), or how Mersenne Primes relate to Perfect Numbers!

-  A report by Rafael M, 5th Form, on a presentation by Zoe Griffiths.