Turkish NMO First Round - 2012 Problem - 36 {Combinatorics}
Source:
July 1, 2012
ceiling function
Problem Statement
k stones are put into 2012 boxes in such a way that each box has at most 20 stones. We are chosing some of the boxes. We are throwing some of the stones of the chosen boxes. Whatever the first arrangement of the stones inside the boxes is, if we can guarantee that there are equal stones inside the chosen boxes and the sum of them is at least 100, then k can be at least?<spanclass=′latex−bold′>(A)</span>500<spanclass=′latex−bold′>(B)</span>450<spanclass=′latex−bold′>(C)</span>420<spanclass=′latex−bold′>(D)</span>349<spanclass=′latex−bold′>(E)</span>296