Question 157
There are 51 senators in a senate. The senate needs to be divided into $n$ committees so that each senator is on one committee. Each senator hates exactly three other senators. (If senator $A$ hates senator $B$, then senator $B$ does *not* necessarily hate senator $A$.) Find the smallest $n$ such that it is always possible to arrange the committees so that no senator hates another senator on his or her committee.