
Math Events Math Events, Competitions, Meetups  Local, Regional, State, National, International 
 LinkBack  Thread Tools  Display Modes 
January 19th, 2011, 06:56 AM  #1 
Senior Member Joined: Oct 2010 From: Vietnam Posts: 226 Thanks: 0  Some questions about International Mathematical Olympiad
1. Let n be a positive number. Let T be the set of points (x,y) in the plane where x,y are nonnegative integers and x+y<n. Each point of T is colored red or blue. If a point (x,y) is red, then so are all points (x’,y’) of T with both x’?x and y’?y. Define an Xset to be a set of n blue points having distinct xcoordinates, and a Yset to be a set of n blue points having distinct ycoordinates. Prove that the number of Xsets = the number of Ysets. 2. Let BC be a diameter of circle W with center O. Let A be a point of circle W such that 0° ? ?AOB ? 120°. Let D be the midpoint of arc AB not containing C. Line l passes through O and is parallel to line AD. Line l intersects line AC at J. The perpendicular bisector of segment OA intersects circle W at E and F. Prove that J is the incenter of triangle CEF. 
January 19th, 2011, 11:26 AM  #3 
Senior Member Joined: Nov 2010 Posts: 288 Thanks: 1  Re: Some questions about International Mathematical Olympiad
Where do you get these solutions from?

January 20th, 2011, 06:38 AM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,270 Thanks: 1958 
Are you asking how one can tackle and solve these particular problems under exam conditions, or how one can find most IMO problems and their solutions on the internet?

January 20th, 2011, 07:35 AM  #5  
Senior Member Joined: Nov 2010 Posts: 288 Thanks: 1  Re: Quote:
 
January 20th, 2011, 08:25 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,270 Thanks: 1958 
Mathematical induction is worth trying if the problem looks as though it might be tackled using it. I hadn't tried the geometry problem before seeing the solution, but it's usually helpful to be aware of a range of theorems. Finding the problems and solutions on the internet can usually be accomplished by use of Google. 
January 20th, 2011, 09:33 AM  #7 
Senior Member Joined: Nov 2010 Posts: 288 Thanks: 1  Re: Some questions about International Mathematical Olympiad
thanks alot

January 22nd, 2011, 12:25 AM  #8 
Senior Member Joined: Oct 2010 From: Vietnam Posts: 226 Thanks: 0  Re: Some questions about International Mathematical Olympiad
btw,what is the smallest number of ages can we participate IMO?

January 22nd, 2011, 01:05 PM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,912 Thanks: 1110 Math Focus: Elementary mathematics and beyond  Re: Some questions about International Mathematical Olympiad
I've looked at a page here and it says ". . . for High School students . . .". I didn't see anything specific but I didn't look too hard.

January 23rd, 2011, 05:36 AM  #10  
Senior Member Joined: Oct 2010 From: Vietnam Posts: 226 Thanks: 0  Re: Some questions about International Mathematical Olympiad Quote:
 

Tags 
international, mathematical, olympiad, questions 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
A problem from 32nd International Mathematical Olympiad  johnny  Math Events  1  September 2nd, 2009 08:55 AM 
A problem from 31st International Mathematical Olympiad  johnny  Math Events  4  September 2nd, 2009 07:06 AM 
International Mathematical Olympiad, year 1971  johnny  Math Events  9  September 1st, 2009 04:44 PM 
The 8th Korean Mathematical Olympiad  johnny  Math Events  5  July 23rd, 2009 03:12 PM 
Some questions about International Mathematical Olympiad  Eminem_Recovery  Algebra  1  December 31st, 1969 04:00 PM 