International Mathematics Olympics Results 2007

Turgon

For those of you crunching numbers here are the results.

Russia came top. They have always produced good mathematicians.

http://www.imo2007.edu.vn/index.php?module=ViewResultByCountry.php

Ricka182

WTF!!! Seriously, people actually study for a math "olympiad"?....I find it hard to call it an Olympiad, but whatever makes them happy...I surely couldn't answer these question....congrats to the winners though...

The following is an excerpt from the questions given in English, on Day 1.....


Problem 1. Real numbers a1, a2, . . . , an are given. For each i (1 i n) define di = max{aj : 1 j i} − min{aj : i j n} and let d = max{di : 1 i n}. (a) Prove that, for any real numbers x1 x2 · · · xn, max{|xi − ai| : 1 i n} d2. ()
(b) Show that there are real numbers x1 x2 · · · xn such that equality holds
in ().


Problem 2. Consider five points A,B,C,D and E such that ABCD is a parallelogram
and BCED is a cyclic quadrilateral. Let L be a line passing through A. Suppose that
L intersects the interior of the segment DC at F and intersects line BC at G. Suppose
also that EF = EG = EC. Prove that L is the bisector of angle DAB.


Problem 3. In a mathematical competition some competitors are friends. Friendship
is always mutual. Call a group of competitors a clique if each two of them are friends. (In
particular, any group of fewer than two competitors is a clique.) The number of members
of a clique is called its size.
Given that, in this competition, the largest size of a clique is even, prove that the
competitors can be arranged in two rooms such that the largest size of a clique contained
in one room is the same as the largest size of a clique contained in the other room.

WanBoy67

4 & 1/2 hours for a maths problem that barely fits half a page

I wonder what an Honourable Mention is? Maybe they were left with a remainder or forgot to carry a one Close but not close enough, I'm afraid we'll have to place you in the 'bit thick' column

Seriously though, some smart people there. We will rely on these people come the Deep Impact like asteroid!

drthtater

Ricka182 wrote:

problems

I can answer those.

Problem 1: Bob

Problem 2: What's that about a quad motorcycle?

Problem 3: That's easy. Pull the fire alarm. No one in the building. Answer is 0

sprkymrk

All I need is an abacus to answer those, noooo problem.

ally_uk

I suck at math lol those questions you posted hurt my brain cells I think I am going to go to bed now as I am really puzzled

larkspur

how would you like to be the russian that received silver and the rest of his peers were gold.

dude go get the peanuts!!!