New Zealand Maths Olympiad Committee online

We had some disappointments in co-ordination yesterday, with a flawed solution we thought deserved at least five or six out of seven knocked back to four; and another otherwise perfect solution to problem four knocked back to six, for not explicitly explaining why weights 2^1, 2^2, …, 2^{n-1} formed an instance of the problem for n-1 (just divide them all by two!). There was little to be done about this, however, as similar rulings had already been applied to other teams; and in fact the point off for no-division-by-two wasn’t entirely unexpected. Aside from that things have gone reasonably well, although we do still have one script for problem five rescheduled for later today.

The day began smoothly, with our appointment for problem three (the hardest problem of day one) scheduled for 9am. We told the co-ordinators that we didn’t think there were any points to be found in our students’ work, to which they agreed, but invited us to discuss their work anyway. There was really only one script where anything substantial had been written, and we explained why its proof that f(x)<=0 for all x (worth two points in the mark scheme) was incorrect. They agreed that “it is not allowed to make this mistake”, and we shook hands on six zeros.

Next up was problem four, at 2pm. The co-ordinators quickly agreed to three of the sevens we asked for, but as we’d expected wanted to look more closely at the other three scripts. One of these used an unusual construction to prove the required recurrence, and we were working our way through this together when our half hour appointment ran out. We were given a new appointment at 8pm, with the points for two scripts yet to be agreed on.

Problem five was next, at 5. We had what we thought were two 7s, a 6 (credit goes to Ilya for identifying this), a 3 and two 2s. All of this was agreed to readily enough, except for one of the 7s, which was written hurriedly during the last fifteen minutes of the exam, and had to be gone through carefully. After a time out to discuss it amongst themselves…and calling over the problem captain…they agreed that it was very good work, but offered six points. The deduction was for a spurious equation which made them question the student’s thinking in reaching the desired conclusion. It was false, but unnecessary, and if you just covered it up, there would be no dispute! Extremely reluctant to accept a 6 we rescheduled in order to review the script further, and today at 10:30 we hope to convince them he did know what he was doing.

8pm brought both bad news and good. It turned out there were other students with the same error as the one in our first script, and the co-ordinators for the problem had met to discuss how to handle it. To our great disappointment the decision there meant we could get only four point. For the second script? “I have good news”, said a co-ordinator, holding up his laptop and showing us some lines of code. “I have implemented his construction, and it works; what’s more, we think that his proof is correct. So we agree with you that he gets seven points.”

So, with three problems co-ordinated so far we have either 63 or 64 points, with at least five perfect sevens, spread between four students. Wish us luck today!