Date: 15 Jul 2004 23:36:31 +0100 From: Adrian Sanders Subject: Re: IMO Well everything is now known. The UK points totals were as follows: Giles Coope 23 bronze David Fidler 24 silver Paul Jefferys 32 gold Martin Orr 22 bronze Alexander Shannon 16 bronze Anne Marie Shepherd 17 bronze These marks were fair. I think some of our students might have done a little better on another day, but getting 6 medals is great. We got full marks on q.4, and solid totals on q.1 and q.2, but rather little elsewhere. The cutoffs were 16, 24 and 32. We came 19th. The top four teams in order were China, USA, Russia and Vietnam. Four students got 42s. I shall provide more complete data (as requested by Joseph) tomorrow morning on our performance and on the IMO scores in general. I just need to find Gordon Lessells... Many of you have emailed me interesting comments about the papers - sorry I haven't had the chance to reply to you individually. I think the consensus around here is that the papers were pretty good. Question 3 was found relatively difficult (< 10 solvers, I think), and q.6 relatively straightforward. I suspect when the data is analysed that q.5 will be found to be a rather difficult one for that position on the paper. The IMO experience as a whole has been excellent, though a somewhat improvisatory sense of organization has prevailed at times. Best wishes to one and all, Adrian On Jul 15 2004, Adrian Sanders wrote: > My apologies; you are quite right, Adrian > > On Jul 14 2004, Joseph S. Myers wrote: > > > On Wed, 14 Jul 2004, Adrian Sanders wrote: > > > > > 2. Find all polynomials P(x) with real coefficients which satisfy the > > > equality > > > > > > P(a-b) + P(b-c) + P(c-a) = P(a+b+c) > > > > > > for all real numbers a,b,c such that ab + bc + ca = 0. > > > > I think there may be a typo here - the version of the question from > > www.mathlinks.ro (which I put up on www.bmoc.maths.org) has an extra > > factor of 2, > > > > P(a-b) + P(b-c) + P(c-a) = 2P(a+b+c). > > > > I've put the bulletin on www.bmoc.maths.org.