I found myself experiencing the strangest sense of déjà vu in the run-up to the second knockout round of the Hans Woyda competition this year. Once again, we were due to host Queen Elizabeth’s School for the quarter final, and once again, when finding a suitable date for the match I had to navigate Olympiads, Chess tournaments and Adavya’s return to the Romanian Master of Mathematics competition after remedy. With few options left before the 24th February deadline, we ended up being forced to schedule the match for the last day of half term, and to avoid keeping everyone from their holiday we came to the unorthodox conclusion that the best time to host the match would be during lunch break. So it was that the SPS team of Haoming (4th), Rafael (6th), Lucas (L8th) and Adavya (U8th) took their seats straight after period 4 to kick off the match. Last year we ended up winning against Queen Elizabeth’s, gaining an early lead and maintaining it until the end of the match, and as the opposing team settled into their places I couldn’t help but wonder; just how long was this déjà vu going to continue?
The first four starter questions all concerned problems related to the Chinese remainder theorem and were deftly handled by both sides. St Paul’s kept up their streak on the next four questions, but two slips from the Queen Elizabeth’s team gave us an early 4 point lead, once again echoing our early lead from last year’s match. The geometry section was up next, but remarkably both sides answered all four questions flawlessly, marking one of the few times no-one from either team has been tripped up by the hemispheres, sectors, triangles and cylinders in front of them! For the mental arithmetic section the teams were tasked with finding, listing and carefully ordering the factors of a given number without writing down a single piece of working. Haoming and Rafael sailed through their questions (despite an initial ambiguity in the wording), but a misunderstanding from the Queen Elizabeth’s side gave Lucas an opportunity to steal a point which he confidently capitalised upon. We now had the opportunity to extend our lead by 3 further points, but a misread by Adavya allowed his opposite number to steal a point back and keep the margin at 4 points total. We then came on to the team question, where both sides had to categorise a set of three-digit numbers and demonstrate Fermat’s Christmas theorem with them by deciding which could be expressed as the sum of two squares (and giving the sum explicitly where appropriate). Both sides filled out most of the sheet, but while Queen Elizabeth’s only left two gaps (as opposed to our four), an incorrect prime factorisation on their part meant that the two teams ended up on the same total score, leaving the overall difference in points unchanged at the halfway mark.
After a stop for cakes and sandwiches (which this time doubled up as lunch for most participants) we settled back down for the calculator round, all of which concerned various approximations to irrational or transcendental numbers. Both sides answered these questions very confidently, with Lucas and Adavya taking advantage of their knowledge of continued fractions to simplify their questions significantly, but a small slip on our side allowed Queen Elizabeth’s to close the gap to 2 points. The algebra questions were up next, all of which concerned integer solutions to factorised equations. Both Year 9’s started strong, but some missed negatives from Rafael let Queen Elizabeth’s steal a point, and with the remainder of the questions answered flawlessly by both sides they had managed to take the lead for the first time this match by a single point. Suddenly, I realised that the pattern from last year was broken. We may have still had a member of the department spectating, but last year it was Adrian Hemery and Andy Ashworth Jones and this year it was Simon Morris instead, and while we started both matches with early leads, by last year’s race section we had never fallen behind and had built up a comfortable margin of points. Could our luck be about to run out?
Fortunately, two things then happened which reassured me that my déjà vu might not be over after all. The first is that the Queen Elizabeth’s coach produced his own set of buzzers for the race questions. It was the excellent buzzers he brought with him last year that I shamelessly copied for this year’s matches, and I was delighted to see that he had brought them again, not least because the buzzers I purchased make such objectively unpleasant sounds. This year he had a new blue buzzer which made a cartoonish “boi-oi-oing!” noise, replacing the green Meet Me in St. Louis trolley bell buzzer from last year, but my déjà vu increased further when the Queen Elizabeth team decided to give us the same purple “Honk! Honk!” buzzer we had used in the previous match!
Finally, we were all set for a full recreation of last year’s ending after the High Master once again turned up to spectate, and despite having just slipped into second place, I had a good feeling as the room went quiet for the first race question. I could feel my heart beating quicker and quicker as the time ticked down for both Year 9’s, but Haoming’s hearty honk gave us the first 2 points and put us back in the lead. However, neither Year 11 spotted the hidden 3-4-5 triangle in the next question, and while Lucas honked first to solve his hidden quadratic, it was the Queen Elizabeth Year 12 that sprung to success after realising that both positive and negative roots still needed to be included, putting them back ahead. Some rapid counting then took place on both sides, but an emphatic honk from Adavya secured the next 2 points and put us narrowly ahead again for the last four questions. Haoming, who had actually forgotten that he had one more question to answer, more than made up for it by honking his way through a quick fraction to decimal conversion, and Rafael then proved that he had revised his surds well by racing through his simplification. A rapid honk from Lucas put us even further ahead, and while both Year 13's answered at a blistering pace it was Adavya's honk that reached my ears first, bringing the match to a close and showing that History really does repeat itself with a decisive 63 - 54 victory for St Paul's.
- Mr Cullen-Hewitt
Could you have spotted the trick to answer this question in under a minute?
