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P16 [Combinatorics] - Turkish NMO 1st Round - 2014

Source:

May 23, 2014

Problem Statement

Asli will distribute 100100 candies among her brother and 1818 friends of him. Asli splits friends of her brother into several groups and distributes all the candies into these groups. In each group, the candies are shared in a fair way such that each child in a group takes same number of candies and this number is the largest possible. Then, Asli's brother takes the remaining candies of each group. At most how many candies can Asli's brother have?
<spanclass=latexbold>(A)</span> 12<spanclass=latexbold>(B)</span> 14<spanclass=latexbold>(C)</span> 16<spanclass=latexbold>(D)</span> 17<spanclass=latexbold>(E)</span> 18 <span class='latex-bold'>(A)</span>\ 12 \qquad<span class='latex-bold'>(B)</span>\ 14 \qquad<span class='latex-bold'>(C)</span>\ 16 \qquad<span class='latex-bold'>(D)</span>\ 17 \qquad<span class='latex-bold'>(E)</span>\ 18