Maths Olympiad Prep

Library / /16 of 16

, 2024

Combinatorics Difficulty 5.0 AIME, harder Prove it United Kingdom

A large number of people arrange themselves into groups of 2, 6 or 10 people. The mean size of a group is 5. However, when each person is asked how many other people are in their group (excluding themselves), the mean of their answers is 7. Prove that there are no groups of 6 people.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.