3. There are 16 members on the Height-Measurement Matching Team. Each member was asked, "How many other people on the team - not counting yourself - are exactly the same height as you?" The answers included six 1's, six 2's, and three 3's. What was the sixteenth answer? (Assume that everyone answered truthfully.)
Solution:
3
For anyone to have answered 3 , there must have been exactly 4 people with the same height, and then each of them would have given the answer 3. Thus, we need at least four 3's, so 3 is the remaining answer. (More generally, a similar argument shows that the number of members answering $n$ must be divisible by $n+1$.)