Hans Woyda Semi Final vs SPGS (Knockout Round 3)

I had been watching the girls’ school’s results so far with growing unease; while the nature of the competition makes it difficult to compare scores between matches, I couldn’t help but notice that they had beaten our totals in the last two rounds, and I had not forgotten the speed and accuracy on display from their squad in the mixed friendly we hosted back in September. However, there was no doubt in my mind that if anyone could give them a run for their money, it was Yidong (4^th), Shyamak (6^th), Adavya (L8^th) and Eason (U8^th). One thing was certain; it would be a thrilling match.

 Both teams started strong on the starter questions, but an early mistake from SPGS gave us a 2 point lead after the first four. I started to imagine that lead snowballing into an insurmountable gap, but in a sign of things to come, a slip on our side in the remaining questions brought the two teams back level. Up next was the geometry section, all of which concerned overlapping isosceles triangles. Yidong and Shyamak made an arithmetic mistake on their first question to give SPGS the lead, and a disagreement about a minus sign between Adavya and Eason meant that we missed out on an opportunity to take it off them. We then moved on to the mental arithmetic and probability section, where the ability to steal points from your opponents makes this a particularly important set of questions. However, a clean sweep from both sides (helped by a very educated guess from Eason on the final question!) kept that from happening and meant that SPGS maintained their 2-point lead.

 The team question tasked them with finding all possible ways of expressing 119 as the sum of three primes. This was described as an application of Vinogradov’s theorem. Still, as a mathematician I can’t help but point out that Vinogradov’s theorem only actually deals with numbers with at least 1347 digits (which, last time I checked, is a few more than 119 has); it is more accurately an application of Goldbach’s weak conjecture. With that needless pedantry out of the way, let us return to the match itself, which saw a valiant effort from SPS with 26 of the required sums and an extraordinary performance from SPGS with 38. However, the peculiarities of the scoring system meant that SPGS only actually got one more mark despite the impressive margin. With an extra bonus mark for winning the section, they had increased their lead to 4 points, or two questions’ worth, and I was starting to feel a little uneasy; the gap between the two teams was still small, but given the ability level of both sides any advantage would be challenging to overcome.

 The calculator section was up next, and all the questions concerned the trajectory of a cannonball fired from a 16th-century Spanish Culebrina (naturally). In a remarkable turn of events, SPGS made two mistakes in this section, and a perfect set of answers from SPS meant that their lead vanished instantly. I was astonished that we were back on level pegging this late in the match, and I could feel my heart racing anew as we entered the algebra and calculus section. These questions all concerned a discontinuous function on the reals, and once again, there was the option to steal points from the other side, which raised the stakes even further. Shyamak couldn’t quite capitalise on an early mistake from SPGS, but he still gave us a 2-point lead by getting his next question right. Adavya managed to steal a point immediately afterward and with correct answers from then on, we had built a 5-point margin going into the race.

 A break before the race began allowed for two quick calculations. First, a simple parity check showed that a tie was already out of the question; whatever happened in the next eight questions, one school would definitely walk away the winner. Second, some straightforward algebra showed that we only needed to get three of the next eight questions right to secure the win. That might sound easy, but remember that in the race, it’s first come, first served. With the two teams so closely matched, a 4-4 split was entirely expected, and it would only take a couple of mistakes to tip that into 6-2 and hand SPGS the victory. You could cut the tension with a knife as the teams fell silent, and without any further delay, we launched into the first question. Both hands flew into the air in quick succession, but the SPGS Year 9 beat Yidong to the punch and handed them the first 2 points. Up next was a question involving finding the maximum value of a quadratic function. Both sides missed the easy trick, and the time ticked down excruciatingly slowly as they diligently worked through the algebra. Shyamak held his course and gave us the first of the three correct answers needed to get us over the finish line. Adavya followed that up with some deft geometry involving circles, tangents, and an emergent trapezium. I started to see the light at the end of the tunnel as we now had five questions left to get one more correct answer. Unfortunately, some lightning-fast binomial expansion from the SPGS Year 13 robbed Eason of the opportunity to settle things there and then, so we returned to Year 9 with four questions to go.

 Both students had clearly solved the next question before it had even been read out, but a misunderstanding from Yidong regarding when he was allowed to start writing handed SPGS the next 2 points. The Year 10 from the girls’ school was also quick off the mark in spotting the odd one out amongst a list of potential squares, and I felt the light fading as we came to the final two questions. Neither Year 12 read the next question correctly, assuming the given numbers were areas rather than side lengths, and as such, we came to the last question still one short of the three correct answers we needed to seal the deal. The score stood at 50 points to SPGS and 51 to SPS, and I felt time stand still as Alexandra Shamloll read out the final question. Both Year 13’s knew each other well and had spent a lot of time together at Zhivko and Simon’s problem-solving sessions, and I saw their eyes light up as they realised that they were being asked to do some simple combinatorics. I knew it was an easy calculation, and speed would be of the essence. I could barely watch as the time started, and in a split second the first hand was in the air. It was Eason’s, and as his correct answer was confirmed I knew that his familiarity with Pascal’s triangle had taken us through to the final for the first time since 2022. It was an ecstatic end to a nail-biting match, and while both teams performed sensationally, we left with a narrow 53 – 50 victory.

I have copied the question with which Eason secured our victory below; could you do it in under a second?

- Mr Cullen Hewitt