Date: 16 Jul 2004 07:15:18 +0100 From: Adrian Sanders Subject: Re: IMO Here is some further information on the IMO - mostly for Joseph's benefit, but it may be of interest to some others of you as well. The full UK results were UNK1 (Coope) 7 2 2 7 3 2 = 23 UNK2 (Fidler) 7 6 1 7 3 0 = 24 UNK3 (Jefferys) 7 7 2 7 3 6 = 32 UNK4 (Orr) 6 7 2 7 0 0 = 22 UNK5 (Shannon) 2 6 0 7 1 0 = 16 UNK6 (Shepherd) 7 1 1 7 1 0 = 17 There was some beautiful stuff from David Fidler. As last year, we were reasonably efficient on the easier questions 1,2,4 - but rather disappointing on the rest, particularly question 5. There were 87 countries participating altogether, including Mozambique (MOZ) and Saudi Arabia (KSA) for the first time. The number of Arab nations was higher than usual - Morocco, Tunisia, Kuwait, Saudi Arabia. Forthcoming hosts were announced: Spain 2008 (unknown location), Germany 2009 (Bremen). Full results for countries were as follows: Albania 57 Argentina 92 Armenia 98 Australia 125 Austria 55 Azerbaijan 72 Belarus 154 Belgium 86 Bosnia and Hercegovina 40 Brazil 132 Bulgaria 194 Canada 132 China 220 Colombia 122 Croatia 89 Cuba 17 (one contestant) Cyprus 49 Czech Rep 109 Denmark 46 Ecuador 14 Estonia 85 Finland 49 FYROM 71 France 94 Georgia 123 Germany 130 Greece 126 Hong Kong 120 Hungary 187 Iceland 35 India 151 Indonesia 61 Iran 178 Ireland 48 Israel 147 Italy 69 Japan 182 Kazakhstan 132 Korea 166 Kuwait 5 Kyrgystan 63 Latvia 63 Lithuania 65 Luxembourg 36 (3 contestants) Macau 86 Malaysia 34 Mexico 96 Moldova 140 Mongolia 135 Morocco 88 Mozambique 13 (3) Netherlands 53 New Zealand 56 Norway 55 Paraguay 13 (3) Peru 49 (3) Phillipines 16 (5) Poland 142 Portugal 26 Puerto Rico 43 (5) Romania 176 Russia 205 Saudi Arabia 4 Serbia and Montenegro 132 Singapore 139 Slovakia 119 Slovenia 69 South Africa 110 Spain 57 Sri Lanka 33 Sweden 75 Switzerland 57 Taiwan 190 Thailand 99 Trinidad and Tobago 29 (5) Tunisia 31 Turkey 119 Turkmenistan 52 Ukraine 174 UK 134 USA 212 Uruguay 47 Uzbekistan 79 Venezuela 15 (2) Vietnam 196 Apologies for spelling errors in the above: some have crept in, I'm sure. UK was third in the EU (Hungary, Poland) and third in the Commonwealth (India, Singapore). The four students with 42 came from Canada, Hungary, Russia and Russia. The UK students are all delighted with their medals, and are now enjoying the post-exam part of the IMO. Adrian + Geoff On Jul 15 2004, Adrian Sanders wrote: > 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.