IMO 2014 Shortlist C2
We have 2m sheets of paper, with the number 1 written on each of them. We perform the following operation. In every step...
Category: Combinatorics
Problem
We have 2m sheets of paper, with the number 1 written on each of them. We perform the following operation. In every step we choose two distinct sheets; if the numbers on the two sheets are a and b, then we erase these numbers and write the number a ` b on both sheets. Prove that after m2m´1 steps, the sum of the numbers on all the sheets is at least 4m . (Iran)