Skip to main content

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.



Popular posts from this blog

The Hans Woyda Trials

The Hans Woyda Maths competition is a London based interschool challenge. A big difference to other competitions is that it is a vertical year group team containing a Fourth, Sixth, Lower and Upper Eighth student (Years 9, 11, 12 & 13). The Hans Woyda’s main focus is speed, with seven sections of fast-paced questions. For instance, in the first section students only have 30 seconds to give their answers, and in the last section the first student to answer correctly gets all the points! The trials took place over multiple mornings and lunch breaks and students had to complete a time pressured test in order to claim a place in the St Paul’s squad. The top 3 students of each year group will each compete in one of the group matches of the Hans Woyda competition and will challenge other schools for the illustrious trophy. Here is a selection of some of the questions:
Read more

Problem Solving with Mykhailo

The maths society had the pleasure of welcoming one of our own, Mykhailo who presented a captivating talk on problem solving in mathematics. He began by telling us of his journey through mathematics, starting in Ukraine at the humble age of 7, where he agreed to compete in his first Olympiad in return for some Lego - a worthy reward. By the age of 11, however, he began to lose interest until a remarkable geometry teacher reignited his passion. From that point on, he was completely hooked on geometry, so much so that his Olympiad scores r eflected his singular focus: 0/7, 0/7, 0/7, and finally, 7/7, as he excelled in geometry alone. He, therefore, decided that it would be best for his progress if he stopped doing geometry altogether, focusing instead on the other 3 areas of math: Algebra, Arithmetic, and Number theory. He led us through a series of questions, seemingly impossible at the face of it but very manageable after explanation. Among the problems were a complex simultaneou...
Read more

Hans Woyda Final vs King's College School Wimbledon

 Yesterday, six months after kicking off the 2024-25 Hans Woyda season with our annual friendly against SPGS, we were at long last on our way to the final. There was a palpable tension around the school site and an unmistakable atmosphere of excitement and anticipation, making it abundantly clear that the entire school had their minds on that afternoon’s Mathematics fixture. As I set off for the match with Yidong (4 th ), Shyamak (6 th ), Adavya (L8 th ), and Eason (U8 th ), accompanied by Dr Stoyanov for moral support and intimidation, pupils and staff had even gathered by the towpath to wish them well; unfortunately, they all seemed to be facing the wrong direction, but it was touching nevertheless. We made our way to the City of London School (which offered its services as neutral territory for the final), discussing tactics on the tube and working through a set of warm-up questions. We met the King’s College School Wimbledon side in the lobby as we arrived, and based on previou...
Read more