Hans Woyda Northern Plate Competition Semi Final WBGS @ QEB
BackHans Woyda Northern Plate Competition Semi Final WBGS @ QEB
Monday 7th February 2022
On the very day that gun salutes began to be fired for the Platinum Jubilee of our Queen Elizabeth II, the WBGS Hans Woyda Competition team (Ray C, Jakub S, Salman S and Hamish S) faced the daunting opposition of a school named after another Queen Elizabeth, QE Boys school in Barnet, in the semi finals of the North Plate competition.
For those unacquainted with Hans Woyda, this is a mathematics competition in which WBGS competes every year, where we send a team of one year 7-9, one year 10-11, one year 12 and one year 13 to compete, each student against their age-equal, at schools across North London. In this year's competition, after some studious preparation at Maths Club every Monday lunchtime we managed to make it to this match having won the last one 34-27. We knew QEB would be a tough opponent but we hoped to be up to the task.
The first round, starter questions, tasks students with completing a relatively "simple" maths problem in 30 seconds. An example question was to find the coefficient of x3 in (2+x)6. Here we dropped 2 points relative to QE, finishing with 16 points to 14 (if my memory serves correctly).
On to the geometry round, which is always a sticking point for aspiring secondary school mathematicians. As usual, the questions proved a challenge with both teams scoring only 4 points (the two Y7-11 questions), to leave WBGS trailing 20-18 (I think!). In one question we were tasked with identifying the difference in areas between two shaded sections formed from concentric semicircles, while another challenging problem revolved around finding unknown lengths and then areas in sectors of a circle.
In the third round, mental arithmetic and probability, having won the coin toss, we deviated from our traditional strategy of going first, hoping to reap the reward of getting the earlier (and usually easier) algebra and calculus questions in round 6. Some questions from this round included calculating the number of possible meals one could order from a menu, and the probability of getting 2 heads from 4 throws on a biased coin. Not too challenging, but in your head, under the pressure of Hans Woyda these questions become a more difficult ordeal. Here we scored a total of 6 points while QE took 9, stealing the point on the probability question due to a silly mistake. Would this prove costly later on?
Going into the team round the scores were then 23-18, QE having opened up a 5 point gap on WBGS. The team question asked us to find as many 24 hour times as possible which, when displayed on a 4 digit 7 segment microwave oven display, would use exactly 14 of the segments. The WBGS team took advantage of the obvious strategy of reordering (permuting) the answers we found to get around 60 possible answers, but sadly this "pro strategy" ended up being high risk, high reward, and led to our downfall. As one of the base answers was incorrect, we had then permuted it several times, generating around 10 incorrect answers. As each wrong answer cancelled out a correct answer, we were left with 22 fewer scoring answers in the round than QE, and so by the brutal scoring system they took 5 points to our 1 in this round. Therefore going into the second half we were down by a whopping 9 points.
After the team question is always the somewhat peculiar calculator round. As there is only 1 question per student and no opportunity to "steal" points from the other team, some have disregarded its interest in Hans Woyda, and yet today it gave us a crucial helping hand. By scoring 6 points to QE's 4 the lead would remain at 7 points, but some effective persuasion of the adjudicating teacher from QE (himself an ex Watford Boy) convinced him that because Salman's unruly surd answer was in fact equal to -10 (on the authority of his calculator), we could have the two points. Hence going into the race we were 5 points off of the lead. This is certainly a substantial margin to recoup, but we knew it was possible, having been on the end of such comebacks in past competitions.
In the race round, with 16 points up for grabs and each question offering a 2 point gain on the other team, anything can happen. Ray solved his first question and slammed the buzzer, scoring 2 points to WBGS. The deficit was now at 3. A tricky Y11 question involving the ratio of areas between a square and a circumscribed hexagon saw neither team gain any points. In the first year 12 question, an unprecedented occurrence of both teams scoring 2 points was recorded when both students recalled the prime factorisation of 2021 almost instantly, something we had memorised and which came up in the previous round. QE were still 3 points ahead. The year 13 question required evaluation of (√3 + 1/√3)3. As our year 9 later pointed out, putting the value inside the brackets over a common denominator yields a shortcut (as is often the way with race round questions), so I shouldn't really have been too smug about my last minute binomial expansion which took us to within 1 point of the lead.
Hence going into the second set of race questions there was a familiar echo of the last match, in which we had to win more race round questions than our opponents to see us through. Unfortunately a calamitous failure to ensure that the buzzer was passed to our year 9 player may have distracted him, leading him to give his answer in the wrong format when he finally had the chance. QE had climbed back to 3 points ahead. With only 6 points left in the match if they won one more question they would seal the victory. Year 11s had to find the lowest number which is one less than a multiple of 30 which is not prime, but alas neither managed it. Now only 4 points were left with the lead at 3. Sadly, a tough algebraic combinatorics question proved too difficult for both year 12s, so with only one question remaining and the lead at 3 the match was decided in favour of QE. That said, an interesting year 13 question asking for a function which is its own second derivative but not its own first derivative had to be played before we could say goodbye. Rather than spot the obvious answer of e-x, I contrairily selected sinh(x), which required a check in the A Level formulae booklet (not given in Hans Woyda) to ensure it was correct. Alas although we scored 2 points on the final question we had a fair idea at this point that we were 1 point behind, so it came as no surprise when Ms Glypti read out the final scores QE 46-45 WBGS.
Overall, it was a cracking effort from the team and a brilliant match to be part of. As there's no 3rd place playoff in the plate, we can consider ourselves equal bronze medallists. We'd like to take the opportunity to thank all those who have represented the school in Hans Woyda this year (and led to this success), all those who have come to Maths Club to practice (do keep coming along; we've still got plenty of fun maths to explore), and especially to the ever-present Ms Glypti who has, throughout this competition, gone the extra mile to ensure we can perform at our best, such as by organising a packed lunch from the canteen to fuel ourselves for today's match. Yueyang and I will be heading off to university next year, but we wish all the best to the team for next year's competition who can hopefully do one better and make it to the final to replicate the success we had 5 years ago.
Hamish Starling & Yueyang Han