The start of the spring term is always a bittersweet moment
in the Hans Woyda calendar. The excitement of moving through to the knockout
rounds is tempered by the knowledge that I will soon have to pick the final
team of 4 from the superb squad of 12 pupils who took part in last term’s group
stage matches. As ever, the selection trials were fiercely contested, and any
of the 81 different possible teams would have stood us in good stead for the
remainder of the competition, but eventually Haoming (4th), Rafael (6th), Lucas (L8th) and Adavya (U8th)
emerged victorious. I had provided each of the team members
with a set of practice questions for the journey which they eagerly worked
through, swapping sheets with each other and comparing methods for the hardest
questions, and at one point Adavya started loudly listing all of the squares
from 162
to 292
to ensure he had them to hand in case he needed them later. The west London
traffic and soporific drizzle had dampened the energy levels slightly by the
time we reached Harrow, but the fresh air and sense of anticipation quickly
roused the team once we had left the taxi, and after a short wait to be
collected from reception we took our seats and the match got underway.
The first four starter questions all concerned the year 2025
(perhaps the result of a minor oversight when the questions were compiled at
the beginning of the year!), and while both sides found them tricky we managed
to squeeze out an early 2 point lead to help settle the nerves. The next four
questions were more straightforward, and after both Year 12’s slipped up on
their harmonic mean question we maintained our slight lead. The geometry
questions were up next, the first two of which concerned some fiddly circle
geometry, and Haoming and Rafael ended their first joint question with
different answers. A single answer is required, so they were given a few
seconds to decide which one to present while the other answers were checked.
Eventually Rafael managed to convince Haoming to agree with him, and luckily
his was the correct answer, the result of which was that we ended that round
increasing our lead to 4 points in total. The mental arithmetic section was
next, and the questions involved calculations using recurring decimals with no
working allowed. This was remarkably well answered by both sides, but after his
coup in the previous round Rafael did slip up on his first question here.
Luckily his Harrow counterpart wasn’t able to steal the point either, meaning
we still had a 2 point lead going into the team question. This involved
Lagrange’s four square theorem which tells us that any integer can be expressed
as the sum of at most four squares. More specifically, Legendre later proved
that all of the numbers that require four squares are of a specific form, and
the teams were tasked with finding the required squares for all of the numbers
of that form between 7 and 159 inclusive. Sadly, 159 is smaller than 162,
otherwise Adavya’s earlier recital would have been extremely useful, but even
so both teams were remarkably successful at working through the list over the
next five minutes. SPS had managed to find a solution for every number while
Harrow had left a gap, which gave me hope that we were going to get the bonus
mark for getting the higher score, but after an error was spotted in one of our
answers (which was negatively marked) Harrow edged ahead, reducing our overall
lead to 1 point.
After a quick stop for refreshments, which Adavya said was
possibly the highlight of these matches, the teams sat back down for the
calculator section. This was another strong round for both teams, and while we
made a units conversion error, Harrow responded with a trapezium rule mistake
which left us 1 point ahead going into the penultimate section. The algebra and
calculus questions all concerned a binary operation, and both sides started
strong. A slip on our side gave Harrow a chance to steal another point, but
they didn’t manage to capitalise on the opportunity, and after their Year 13
made the only other mistake this round Adavya pounced on the chance to increase
our lead to 2 points. This put us slightly ahead for the race, but it also put
us in danger of ending on a draw. Lucas, trying his best to tempt fate,
insisted that this shouldn’t be possible, but after we pointed out that both
sides could fail to score on a question he realised that parity was really the
only relevant concern. At this point, I produced my secret flourish; the two
quiz buzzers I had recently purchased after being inspired by last year’s match
against Queen Elizabeth’s School. Unfortunately I hadn’t been able to hear the
noises they would produce before ordering them online, and I accidentally
bought some of the most annoying buzzers I have ever heard. The choice was
between a harsh, elongated buzzing noise and a loud, extended siren. Harrow
opted for the siren on the basis that it was the more annoying sound, and they
wouldn’t want to have to lose a question and hear it simultaneously. After the
room had settled and the buzzers had been primed we prepared to start on the
race. Haoming shot out of the gate with the first buzz, but a calculation error
gave Harrow the remainder of the time to calmly work their way to the right
answer and draw level on points. Rafael was up next and answered similarly
rapidly, but this time he stuck the landing to bring us back 2 points ahead.
Unfortunately, Lucas was beaten to the punch in the next question which brought
us back to a tie, and a transcription error in Adavya’s answer let Harrow take
the lead. The questions cycled back to the Year 9’s, and Harrow was first to
spot the trick, meaning that they had extended their lead further to two questions.
Rafael, deciding that fate hadn’t been tempted enough already, subsequently
asked if he was right in thinking that if he got his question wrong Harrow will
have won the match. The Harrow teacher confirmed that he was correct, but I
clarified that if neither side got the points a tie would still be possible.
Rafael was first to answer again, but a slight miscalculation resulted in an
agonising wait for the time to run out to see if his prediction would come
true. Luckily the Harrow Year 11 didn’t get the right answer either, but both
Lucas and Adavya needed to answer correctly to keep us in the competition. Once
again, Harrow spotted the trick first for the Year 12 question, and my heart
sank as the answer was checked, but a silly mistake meant that Lucas now had
all the time in the world to work through the problem systematically. Luckily,
he avoided the same error and kept us in the running for one more question. I
could almost sense the intensity of Adavya’s mental exertions during the final
race question, and I held my breath after he buzzed first, but with a
melancholy smile the Harrow teacher confirmed that he had got the answer
correct, and as Adavya strode across the room, arms aloft in celebration, I
realised that for the first time in my Hans Woyda career I was about to witness
to a tie break.
The tie breaker is made up of four more race questions, one
for each year group. A tie in the tiebreaker would be settled by the toss of a
coin (or in this case the roll of an oversized foam die), something which we
really wanted to avoid. Haoming was up, and it was another question with a
trick at the heart of it; both sides took a little while to spot it, but this
time Haoming got there first, putting us 2 points ahead. Next was a variation
on a completed square form question, but while Rafael spotted the general idea
first he missed two of the other squares in the expression, allowing Harrow to
draw level again. Neither Lucas nor his opposite number could solve the circle
question they were presented with, but after the Harrow teacher and I both
berated them for missing the obvious 3-4-5 triangle it was pointed out that we
had actually made the same mistake as the question setter, and the real
(unintended) solution was a lot more fiddly. It was decided to move on
regardless, but once again it all came down to the final question. It was a
classic, involving a geometric series with common ratioi,
but you had to be careful to land on the right remainder modulo 4. Adavya
buzzed first, and time slowed to a crawl as I waited to see if he had made the
right calculation or if the pressure had caused him to go with the obvious trap
(namely assuming that the terms summed to 0). The Harrow teacher paused, and
then announced thati-1
was indeed the correct answer. I collapsed in my chair as Adavya once again
burst from his seat in celebration, and so it was that we ended up making it
through to the quarter finals with a final score of 51-49.
