Maths Olympiad Prep

Library / /70 of 99

, 2015

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

Four problems were attempted by 100 contestants in a Mathematics competition. The first problem was solved by 90 contestants, the second by 85 contestants, the third by 80 contestants and the fourth by 75 contestants. What is the smallest possible number of contestants who solved all four problems?

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.