Acabei de receber isso em outra lista.. Agora vou tentar fazer (provavelmente sem sucesso :) e depois mandar meus comentarios pra gente debater na lista! Abracos, Marcio -----Mensagem original----- De: Mojca Miklavec [mailto:[EMAIL PROTECTED]] Enviada em: Domingo, 8 de Julho de 2001 15:41 Para: [EMAIL PROTECTED] Assunto: [imo-problems] IMO 2001 Problems, First Day 1. Let ABC be an acute-angled triangle with circumcentre O. Let P on BC be the foot of the altitude from A. Suppose that <)BCA >= <)ABC + 30°. Prove that <)CAB + <)COP < 90°. 2. Prove that a/sqrt(a^2+8bc) + b/sqrt(b^2+8ca) + c/sqrt(c^2+8ab) >= 1 for all positive real numbers a, b and c. 3. Twenty-one girls and twenty-one boys took part in a mathematical contest. - Each contestant solved at most six problems. - For each girl and each boy, at leat one problem was solved by both of them. Prove that there was a problem that was solved by at least three girls and at leat three boys. imo-problems is part of the IMO network, http://imonet.online.fr/ remember to go there and add your name ! ---- To receive these messages in a daily digest, email [EMAIL PROTECTED] To stop recieving these messages, email [EMAIL PROTECTED] You can always view and reply to messages on-line, at http://www.egroups.com/group/imo-problems For more help, email [EMAIL PROTECTED]
