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Three sixth-formers have qualified for the next stage of the élite British Mathematical Olympiad after strong performances in the first round.

Bashmy Basheer, Nico Puthu and Niam Vaishnav, all of Year 13, were among nine boys to reach Round 1 of the Olympiad, which is itself one of the follow-on rounds of the UK Mathematics Trust’s Senior Maths Challenge. They won a certificate of distinction and a bronze medal, with Nico scoring 40 out of 60 and both Bashmy and Niam scoring 37.

They now progress to Round 2, where success results in an invitation to participate in training to represent the country in the International Mathematical Olympiad.

Assistant Head of Mathematics Wendy Fung congratulated the three on their achievement in the first round and wished them success in Round 2.

Their fellow Year 13 pupils, Kiran Aberdeen, Kishan Patel and Robert Sarkar, also achieved a certificate of distinction. The remaining three sixth-formers all achieved a certificate of qualification in Round 1, which consisted of six long, extended questions to be completed in three-and-a-half hours.

A further 29 sixth-formers took part in the Senior Maths Challenge’s other follow-on round, the Senior Kangaroo, which represents an increase on the 2017 total of 25 and the 2016 figure of ten.

Thirteen boys were each awarded a merit certificate for scores of 35 and above. Saruthan Seelan (pictured above right) in fact achieved double this total, with his score of 70 out of 100 making him the best in Year 12.

Sehj Khanna (left) was the highest scorer in Year 13 with 50/100.

The Senior Kangaroo is a one-hour paper, with all the questions requiring three-digit. Certificates of merit are awarded to the top 25%.

A QE boy’s correct answer to an outlandish numerical and scientific challenge won him a prize during a show aimed at inspiring young mathematicians.

Aryan Shrivastava correctly calculated that 7.5 million tins of Alphabetti Spaghetti would be needed to list the entire human genome, netting him a signed copy of Helen Pilcher’s book, Bring Back the King, which looks at the science that makes the resurrection of extinct animals a real possibility.

Helen, a scientist, comedian and writer for the science magazine, Nature, was the host for The Maths Inspiration Show at London’s Piccadilly Theatre, which was attended by around 60 Year 11 boys from QE.

She explored the distribution of letters found in a tin of Alphabetti Spaghetti. Her hypothesis was that there should be a strong correlation between the letters found in a tin and the occurrence of letters in the English language. In fact, the scatter graph she produced showed no correlation, nor did others for different languages, reported Mathematics teacher Phillip Brady.

Mr Brady said that Hugh Hunt, who is a lecturer at Cambridge University “put us all in a spin discussing the motion of balls, wheels and tops. He demonstrated how the gyroscopic effect can be used to rotate spacecraft and described why boomerangs come back (as well as demonstrating his boomerang-throwing skills).”

And he added that added that another speaker, Ben Sparks, who visited QE last year to speak to Year 10, took inspiration from Sting’s song, Shape of my Heart (about a poker player) to discuss some probability “whilst warning us of the perils of gambling. He was safe in his bet that in a random selection of 60 of the audience of 15 to 17 year-olds: there was at least one pair who shared a birthday.”

Matt Parker, who describes himself as a “stand-up mathematician”, related some of the mathematical errors set out in his book, Humble Pi. Some, he said, were simply amusing or embarrassing, such as McDonalds miscounting the combinations of meal deals and Pepsi underestimating the value of a fighter plane. However, he pointed out that some other mistakes he had come across could have more serious consequences, such as an aeroplane running out of fuel because the wrong units had been used to fill the tanks.

Afterwards, the pupils reflected on their favourite speakers of the day. Priyan Solanki said: “Hugh Hunt’s demonstration of the gyroscopic precession was very interesting.” (Precession is a change in the orientation of the rotational axis of a rotating body.) Harrishan Kangatheepan enjoyed Matt Parker’s explanation of how our minds can deceive us, especially with enormous numbers such as a trillion, while Ridwan Khan’s interest was piqued by Ben Sparks, from whom he learned aspects of probability that were new to him.

Communication and teamwork skills as well as mathematical ability were key requirements at the regional round of the Senior Team Maths Challenge.

The four-strong QE team scored 164 points out of a possible 172 in the closely fought event hosted by City of London School.

Representing QE in the competition run by the UK Mathematics Trust and the FMSP (Further Mathematics Support Programme) were Edward Hu, Bhavesh Patel, Suvir Rathore and Saruthan Seelan, all from Year 12.

The competition offers pupils an alternative way to express and develop their enjoyment of Mathematics, as well as developing teamwork and communication.

There were three rounds:

• In the Group round, ten questions had to be solved in 40 minutes
• In the Crossnumber, one pair of competitors was given the across clues and the other pair the down clues, although several clues were interlinked
• In the Shuttle, pairs answered questions alternately, with the answer to the previous question providing crucial information for the following one.

The QE team came sixth out of the 30 teams who had entered. First place went to Highgate School, second to Dame Alice Owen’s School and third to the hosting independent boys’ school.

Team captain Edward Hu said “We had a great day competing against and meeting other mathematicians. It was fun and we really enjoyed the Crossnumber, but were obviously disappointed not to progress further in the competition.”

Speakers at the Maths in Action lectures introduced Sixth Form mathematicians to aspects of the subjects not necessarily covered in the A-level syllabus – and even enlisted the seasonal help of the song, The 12 Days of Christmas.

Sixty-five Year 12 boys attended the event at the Emmanuel Centre in Westminster, which was organised by The Training Partnership, an educational organisation specialising in study days at GCSE and Sixth Form level. This year’s lectures were:

• The 12 Days of Christmaths: Kyle Evans, maths musician, 2016 winner of the FameLab science communications competition
• How to build a 1,000mph car: Rob Bennett, Bloodhound SSC
• The Maths of weather and climate: Emily Shuckburgh, British Antarctic Survey
• Windmills of your mind: Dr Ben Sparks, University of Bath
• Closing the gap/ the quest to understand prime numbers: Dr Vicky Neale, University of Oxford.

QE’s Head of Mathematics Jessica Steer said: “Each lecture was inspiring in its own way and has encouraged the boys to delve deeper into the topics they found most engaging on the day. These lectures are a very good way of introducing branches of Mathematics and ways of mathematical thinking not in the curriculum and of showing the range of applications to which the subject can be applied.”

In his lecture, Kyle Evans investigated how many presents in total you receive from the song, The Twelve Days of Christmas. He demonstrated that the presents of which you would get the most were the ones in the middle of the song, on the sixth and seventh days (geese and swans respectively). He linked this to Diophantine equations, where the output must be a whole number. He also discussed Pascal’s Triangle and how one of the diagonals gives the total amount of presents you get each day.

QE delegate Adam Hassan said: “It was very engaging and interesting, as we were trying to work things out, rather than just listening to information – I also learned some good Maths tricks.”

Rob Bennett used his lecture – How to build a 1,000 mph car – to show how Mathematics can be used to solve problems. He talked about conventional wisdom and how humans continually push the boundaries by refining small features. He said that Mathematics will be used in the future to solve problems we do not even know exist yet.

“I liked this talk as I enjoyed the explanation about thermodynamics and how they have improved the car and the design of it,” said Year 12’s Dylan Vekaria.

In her lecture, Emily Shuckburgh, looked at mathematical modelling within the context of climate change, introducing the audience to a model where the Earth is assumed to be a ‘blackbody’ sphere (that is, one that absorbs all electromagnetic radiation falling on it), in order to estimate the surface temperature of the Earth. This model gives an under-estimate, but it is quite close to the true value, she said. A further model introduced an atmosphere and, more importantly, the effect of greenhouse gases, resulting in an estimate of the Earth’s surface temperature that is very close to the true value. She thus showed how this emphasised the importance of starting with a simple model at first and then building up to more complicated, more realistic models.

“The Maths of weather and climate showed effectively how easily understood ideas can be used to build complex mathematical models of real-world phenomena,’ said QE sixth-former Vincent Tang.

In his lecture, Ben Sparks started with the assertion that circles and spirals are everywhere in Mathematics, even though sometimes they are hidden at first. He then moved on to a discussion about rational and irrational numbers. He also talked about the mathematician, Mandelbrot, who decided to start at zero, square it and then add a constant over and over again. He explored what happened with different constants and whether or not the path of each constant converged to zero. The result was the Mandelbrot set, which boys were shown on the projector. Ben zoomed in on one section, but the shape never changed. Instead it kept repeating itself even after being zoomed in. Eventually, the computer was unable to zoom in any further, but this was due to the computer’s lack of ability to do so, rather than the shape of the set, Ben explained. The concluding message was that sometimes we should do Mathematics just because it is “cool and interesting”.

QE attendee Alejandro Lynch Gonzalez said: “I liked Windmills of your mind as it emphasised the beauty of Maths. I found it was the most engaging in terms of looking at the bigger picture and seeing how Mathematics is universal in its laws and properties by looking at its influence on nature.”

Vicky Neale commenced with the Euclidean proof of why there are infinitely many prime numbers, which, she said, is a very old proof. The boys were then introduced to the idea of a ‘conjecture’, which is a statement that has not yet been proved or disproved. A famous example of a conjecture is the Twin Primes Conjecture, which states that there are infinitely many pairs of prime numbers that differ by 2. For a period, mathematicians thought that it was impossible to solve, until one mathematician, Yitang Zhang, proved that there are infinitely many pairs of primes that differ by at most 70 million. Mathematicians since Zhang have been revising and further revising his proof to reduce the number that the primes can differ by, lowering the number to 4,680 and then to 600 and currently to 246. Vicky concluded with the idea that if there is a problem you are having difficulty solving, you should try thinking about a problem you can solve that can help – or even thinking about a problem that you cannot solve but which, if you could solve it, would help with the problem at hand.

“‘I liked this lecture as it was about an interesting bit of new Maths that everyone could understand but hasn’t been solved yet,” said QE boy Ben Domb.

Two QE sixth-formers scored maximum marks in this year’s UK Senior Maths Challenge.

Bashmy Basheer and Nico Puthu, of Year 13, both scored 125 out of 125, earning themselves jointly the Best in School title. They were amongst 39 QE boys to receive gold certificates – up from 33 last year.

A further 55 boys were awarded silver, and 29 bronze. The top 40% of participants in the competition are awarded gold, silver and bronze certificates in the ratio 1:2:3.

The Best in Year 12 title went to Suvir Rathore, who scored 102.

Nine boys, including Bashmy, Nico and Suvir, have qualified for the British Mathematical Olympiad and a further 30 go through to the competition’s other follow-on round, the Senior Kangaroo. To qualify for the Olympiad, candidates must score at least 102 points, while for the Kangaroo, they need at least 83 points.

Nico said: “There were lots of geometry questions, which I found really interesting to solve.”

Congratulating the successful competitors, Assistant Head of Mathematics Wendy Fung said: “Many of the boys who have qualified through to the follow-on rounds have been members of QE’s Élite Maths group for a number of years and are now passing on their experience and wisdom through mentoring students in Years 9 to 11.”

• Sample question:
  The positive integer 2018 is the product of two primes. What is the sum of these two primes?
  A 1001 B 1010 C 1011 D1100 E 1101
  Answer:
  2 + 1009 = 1011 so C

Twelve sixth-formers heard two lectures from mathematicians chosen for their distinction in the subject and their communication skills.

The Year 12 boys heard Dr Jennifer Rogers, from Oxford University, and Dr Katie Steckles, of schools outreach organisation, Think Maths, deliver this year’s London Mathematical Society Popular Lectures at Bush House.

In her talk, entitled Living is a Risky Business, Dr Rogers explained that we are bombarded with statistics every day and that it is therefore important to be able to discern the truth behind a shock headline.

She discussed, for example, the statistics behind the newspaper headlines about bacon sandwiches causing a higher risk of cancer and being equally as bad as smoking. She explained that there is a 1 in 80 lifetime risk of being diagnosed with pancreatic cancer so scaling this up, this is the same as a 5 in 400 risk. A 20% increase would therefore mean that the lifetime risk of getting pancreatic cancer is now 6 in 400.

The headlines only considered statistical significance without quantifying it in any way. For comparison, there is a 4 in 400 chance of being diagnosed with lung cancer if you have never smoked. Smoking more than 25 cigarettes a day increases that to 96 in 400 as you are 24 times more likely to be diagnosed with cancer. Both results (bacon and smoking) are statistically significant but they do not pose the same risk as each other.

Afterwards, one of the QE Year 12 audience, Nico Puthu, said: “I’m really pleased to find out that it’s perfectly safe to eat as much bacon as I want!”

Dr Rogers finished by explaining her dealings with Ryanair. As Vice President of the Royal Statistical Society, she was asked by the TV programme, Watchdog, to investigate the claims by Ryanair passengers that if they did not book seats in advance (and pay for this privilege), then they were always given a middle seat. Four researchers booked four different flights and all were allocated middle seats. She calculated that this would have a probability of 0.2% which suggests that seat allocation is not random. Ryanair, after many denials, finally admitted that their seating algorithm was not random.

QE attendee Sahil Shah said “I enjoyed hearing about her battle with Ryanair,” while Mudit Tuslianey added: “Dr Rogers’ talk linked well to what we have been studying at A-level.”

For her lecture, Dr Steckles spoke on The Greatest Unsolved Puzzles in Maths. One of her demonstrations involved taking a piece of A4 paper and folding it three times, always folding along the longest edge, and then cutting off all four corners of the resulting shape. How many holes will you have made in the A4 paper when it is unfolded? she asked. (Answer: three). This led on to the introduction of the Euler brick which is a cuboid which has integer lengths and integer face diagonals. Some examples are shown in the image here.

Mathematicians are currently searching for the perfect cuboid which is an Euler brick that also has an integer body diagonal, Dr Steckles explained.

QE’s Assistant Head of Mathematics, Wendy Fung, said: “She finished by saying that all the unsolved problems that currently exist will be solved by people who, when they see a puzzle, don’t give up.”

Akshat Sharma and Aadi Desai spoke afterwards of their appreciation of the puzzles she set. Their classmate, Kiran Aberdeen, said: “I found Dr Steckles’ talk very amusing.”