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Hans Woyda Semi Final vs Haberdashers

Déjà vu was a feature of the last Hans Woyda match report, and fittingly enough it reared its head again in Tuesday’s Semi Final against Haberdashers’ Boys’ School. This time, we have to go back to the 2023-24 Semi Final, when we welcomed Habs into St Paul’s for an exceedingly close game. In that match, St Paul’s were either tied or in the lead throughout, until Habs edged in front for the first time in the penultimate question and held off our U8th on the last question to extend their lead even further, knocking us out of the competition with a final score of 53 – 49. Two significant changes gave me hope that history wasn’t about to repeat itself. First, we were the ones making the long journey to the outskirts of Watford this time, as hosting duties had fallen to Habs for this match. Second, none of the current SPS team of Haoming (4th), Rafael (6th), Lucas (L8th) and Adavya (U8th) had been involved in that tragic loss. As the voyage northwards came to an end and we made our way into the match venue, I couldn’t help but wonder; would it be enough to change the outcome?

 The first four starter questions got us off to a shaky start, with two slips giving me a sinking feeling in the pit of my stomach, but an equal number of mistakes from our opposite numbers stopped them from claiming an early lead. There were a couple more mistakes on the next four questions with both sides confused by some fiddly units conversions, but a lucky guess by Adavya put us ahead by 2 points to help settle the team’s nerves. Up next was the geometry section, with a delightful set of questions involving various Pythagorean triples disguised inside larger polygons, and a clean sweep from SPS allowed us to extend our lead to 6 points. This was followed by a selection of mental arithmetic questions, where a mistake on a definite integration by both Year 13s resulted in Habs narrowing the gap to 4 points (after Adavya had verified that he was in fact wrong with a calculator) due to the peculiar priority marking system of this section. However, a perfect set of answers from both sides to the team question (where they were tasked with finding all the different ways of expressing 32 as a sum of squares) allowed SPS to maintain this slim lead into the halfway point of the match.

 As usual we stopped for snacks and refreshments, but the number of biscuits and chocolate bars left untouched as the teams settled back into their seats for the calculator section suggested an inversely proportional relationship between the stage of the competition and the competitors’ half-time appetites. The questions themselves concerned ancient Indian and Babylonian approximations for ,  and , and unfortunately the complexity of the formulae involved confused the majority of our team, with Lucas’ calculator flat out refusing to evaluate the expression he had typed into it. Only Adavya managed to answer his question correctly, cutting our lead from 4 points to 2. The algebra questions had actually been designed by my opposite number from Habs and involved an ingenious function of functions, spitting out the difference between the maximum and minimum of a given function over a specified interval. There were a few slips from both sides here, but again the priority system worked against us, and by the start of the race Habs had drawn level for the first time in the match so far.

 I could feel a prickly sensation running down the back of my neck as we prepared to kick off the final section of the evening. We had been in the lead for the entire match, but Habs had persevered and finally managed to close the gap. Were we about to see a repeat of the climax to our last encounter? I reassured myself that the race is historica
lly our strongest section, but I couldn’t help but remember that it was the race that proved our downfall back in 2024. I could at least take comfort in the knowledge that, while we may not have been on home turf, the SPS team were sure to be buoyed by the warm familiarity of my hideously grating buzzers. Without any further ado, we kicked off the race, with both Year 9s searching for a selection of three-digit numbers with a digit sum of 6. Unfortunately, Habs beat us to it, but there was further upset when it became apparent that the diagram for the next question had accidentally been displayed on the board alongside the text of the first question. It was eventually agreed that we would award full points to both teams and revisit the issue if the margin was a single question or less at the end of the match, but it did nothing to ease the mounting tension in the room. The Year 12s were up next, and some rapid binomial expansion allowed Habs to extend their newfound lead to two questions. Fortunately, Adavya answered the next question within a split second, coming to the sensible conclusion that any convoluted expression involving multiple trigonometric functions probably simplifies to 1, and as such we were back within striking distance as we approached the final four questions of the match. I watched with bated breath as both Year 9s raced to evaluate a product of prime powers, and we were almost robbed when Haoming found himself without the buzzer by his side, but the Habs coach accepted a shout of “Where’s the buzzer?!” as an acceptable method of submitting an answer, bringing us level again with three questions to go. Rafael raced to an answer next, but before it had even been checked he realised that he had misread the question, leaving his opposite number with the remainder of the time to methodically work towards the correct solution. The Year 12s then had to search through their knowledge of three-digit squares, but Habs managed to get there first, putting them 4 points ahead with one question to go. It was impossible to draw level, but if we could bring the gap down to 2 points we could argue for a tie break question to make up for the lost question at the beginning of the section, and so once again our hopes rested on Adavya’s inimitable shoulders. He buzzed first, and time seemed to slow to a crawl as the Habs coach approached to verify the answer. Unfortunately, the pressure to answer first had led to a mistakenly evaluated fourth power, and while the Habs Year 13 failed to answer the question as well it was sadly too late to salvage our chances. I felt the ironic sting of a cruel twist of fate as I realised that Habs had once again knocked us out of the competition with an identical final score of 53 – 49.

 Please do congratulate the boys when you see them; they put in an incredible performance against equally incredible opponents, and it really could have gone either way. That sadly brings our 2025-26 Hans Woyda season to a close, but I have high hopes that we will be able to bring the trophy back to its rightful place in the Maths resource room next year. In the meantime, I have attached the questions as usual, and below is the definite integral that the two U8ths couldn’t quite manage to do in their heads; could you evaluate it in under 60 seconds without any working? 

- Mr Cullen-Hewitt


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