Hello fellow Brilliantians!
As most of you know, the IMO is one of the biggest and most famous of all international Maths Olympiads. Following are the problems which appeared in the test at the end of the First Training Camp of Pakistan for the IMO 2017. Enjoy!:
Let be a triangle. Let be the feet of the perpendiculars from to , to and to respectively. Let and be the feet of the perpendiculars from to and respectively. Prove that are collinear.
Find the number of ordered pairs of sets such that .Compute the answer for .
and are the same pair if and .
or can be an empty set (the pairs in which either one of is an empty set are to be counted as well)
Let be two positive integers (not necessarily distinct) and let be a prime such that .Prove that
denotes the Least Common Multiple of the numbers and .
Find all polynomials with real coefficients such that the polynomial is constant.