Math Forum :: View topic – IMO Test 2 (CHKMO)

I think it is test 3 instead of test 2 Problem 1-need some time to think, most people proved it by induction, though there is a simple “primary school method”. Problem 2-the result’s almost trivial. The problem is how to organize your solution. Problem 3-an extremely easy geometry. It has got many solutions, including trigo, vector, pure geometry, coordinate(not complicated), etc. For trigo and pure geometry, a huge variation of the solutions can be found. For instance, you can use Carnot’s Theorem, Ceva’s Theorem, showing that the two segments are equal in length(i hope u know what 2 segments I’m referring to, anyway, there are many ways to prove them equal in length), etc.

Problem 4-hardest problem of the test (at least it’s what I think), one may be misled that only one function exists, ie f(n)=n.