A large number of people arrange themselves into groups of , or people. The mean size of a group is . However, when each person is asked how many other people are in their group (excluding themselves), the mean of their answers is . Prove that the number of groups must be a multiple of .
Sign in or create an account to reveal answers, view the solution, and save your progress. Create a free account to unlock practice and keep track of your work.
Hamilton Mathematical Olympiad (2024)
One puzzle per day. Cryptarithm, Magic Square, Summit. No sign-up required to play.
Play daily puzzle →Interactive problems and curated lessons—water pouring, magic squares, knight's tour, and more.
Browse library →See how you rank. Top solvers by problems solved correctly. Sign in to climb the ranks.
View leaderboard →