Each member of a group of 37 students was sent to one of three rooms.
Later, each was asked "How many other students were in your room?" The average of these responses was 12.
How is this possible?
If there are N students in a room then each student in that room will answer N-1. (Note the word "other" in the question.)
An even distribution of 12,12,13 will result in an average of (12*11+12*11+13*12)/37 = 11.35, so we know the problem is not outright impossible.
Playing around with the numbers I find a distribution of 9,12,16 gives an average of (9*8+12*11+16*15)/37=12.
Solution
