Question 158
There are 17 people at a party, and each has a reputation that is either $1, 2, 3, 4$, or $5$. Some of them split into pairs under the condition that within each pair, the two people's reputations differ by at most $1$. Compute the largest value of $k$ such that no matter what the reputations of these people are, they are able to form $k$ pairs.
Proposed by: Albert Wang
Proposed by: Albert Wang