From jscholes@kalva.demon.co.uk Thu Nov 12 11:04:01 CST 1998 Article: 220607 of sci.math Path: news.math.niu.edu!husk.cso.niu.edu!vixen.cso.uiuc.edu!uwm.edu!newsfeed1.earthlink.net!news.idt.net!news-peer.gip.net!news-lond.gip.net!news.gsl.net!gip.net!nntp.news.xara.net!xara.net!dispose.news.demon.net!demon!news.demon.co.uk!demon!kalva.demon.co.uk!jscholes From: John Scholes Newsgroups: sci.math,rec.puzzles Subject: IMO problems Date: Thu, 12 Nov 1998 10:44:15 +0000 Organization: NA Message-ID: NNTP-Posting-Host: kalva.demon.co.uk X-NNTP-Posting-Host: kalva.demon.co.uk:158.152.30.114 X-Trace: news.demon.co.uk 910867503 nnrp-06:27845 NO-IDENT kalva.demon.co.uk:158.152.30.114 X-Complaints-To: abuse@demon.net MIME-Version: 1.0 X-Newsreader: Turnpike (32) Version 3.05 <3INQIyYMxegFhuFcUbm2MuR0gQ> Lines: 37 Xref: news.math.niu.edu sci.math:220607 rec.puzzles:114611 Apart from 1980, the International Mathematical Olympiad (IMO) has been held every year since 1959. It usually consists of two papers, each with 3 hard problems and a time limit of 4 - 4 1/2 hours, which require only elementary maths as prerequisites (nothing at undergraduate level). No calculators are allowed. The top competitors usually get close to a perfect score. So if you are really good at this kind of thing a problem should take 1-2 hours to solve. I have now collected all 235 problems. Solving them is proving time- consuming (but fun). A substantial proportion of them have taken me significantly longer than 1-2 hours! I currently have 32 outstanding. There are a few really easy ones, but less than 5 per cent. The average level is significantly harder than the Russian problems. A solution is usually quite short (maybe half a page or a page). For most of them there is a key idea which you have to grasp and then it is easy. The web site http://www.kalva.demon.co.uk gives the problems by year with solutions (where I have them). It also gives them in random order without solutions and with obvious clues as to year removed. [A small percentage of the problems use the year in the problem statement. There is rarely anything critical about the precise number, the salient feature is typically something like the fact that it is a multiple of 3, so I have changed the number where possible.] I am proposing to post the problems in this random order at the rate of one a week. After a week I will reveal the year it was set, so that the solution can be easily found on the web site. Would this be of interest to anyone? -- John Scholes