Counterexample — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Counterexample — a logic concept — each with a professionally curated solution, many with a video solution too, from LIVE by Po-Shen Loh. Browse all concepts or the full past-contest archive.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
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These problems’ difficulty ratings come from real solve attempts on our platform. Tap a band or a contest to filter the list below, and tap a selected band again to include all difficulties. See the full difficulty guide.
AMC 10
2001 AMC 10 Problem 12 • 2003 AMC 10A Problem 6 • 2014 AMC 10A Problem 7 • 2017 AMC 10B Problem 3 • 2019 AMC 10B Problem 2
AMC 12
1951 AMC 12 Problem 10 • 1951 AMC 12 Problem 21 • 1951 AMC 12 Problem 27 • 1958 AMC 12 Problem 44 • 1959 AMC 12 Problem 3 • 1959 AMC 12 Problem 6 • 1959 AMC 12 Problem 14 • 1959 AMC 12 Problem 47 • 1961 AMC 12 Problem 4 • 1964 AMC 12 Problem 12 • 1965 AMC 12 Problem 26 • 1965 AMC 12 Problem 30 • 1966 AMC 12 Problem 22 • 1967 AMC 12 Problem 7 • 1967 AMC 12 Problem 28 • 1970 AMC 12 Problem 17 • 1973 AMC 12 Problem 5 • 1974 AMC 12 Problem 14 • 1975 AMC 12 Problem 3 • 1975 AMC 12 Problem 21 • 1977 AMC 12 Problem 11 • 1982 AMC 12 Problem 7 • 1984 AMC 12 Problem 18 • 1986 AMC 12 Problem 4 • 2003 AMC 12A Problem 6 • 2015 AMC 12A Problem 13 • 2016 AMC 12A Problem 5 • 2017 AMC 12B Problem 2 • 2019 AMC 12B Problem 2 • 2020 AMC 12B Problem 23