In pigeonhole questions (and this question), you're given a total number and a number representing the amount of 'containers'
That is, the pigeonhole principle states that if items are put into containers, then at least one container must contain more than one item.
By that definition, you want to find out how many of an object (in this case, votes) goes into each 'container' and the remainder. In this case, it states that 'once candidate received more votes than anyone else and so became the new president.'
Hence, seen through @jimmysmith560, 3543/15 = 236 and 3/15 ... since one must have more votes than the rest, it can't 237 ... +1 so answer is 238