Maths Olympiad Prep

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Problem 913

AMC 12 late, AIME early
Combinatorics Difficulty 4.0 Find the answer BMO Round 1 · United Kingdom · 2010

Isaac attempts all six questions on an Olympiad paper in order. Each question is marked on a scale from 00 to 1010. He never scores more in a later question than in any earlier question. How many different possible sequences of six marks can he achieve?

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