Floor and ceiling functions — AMC & AIME Problems
Practice every real AMC 8, AMC 10, AMC 12, and AIME problem that uses Floor and ceiling functions — a algebra 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 8
1990 AMC 8 Problem 13 • 1991 AMC 8 Problem 17 • 1999 AMC 8 Problem 17 • 1999 AMC 8 Problem 18 • 1999 AMC 8 Problem 19
AMC 10
2003 AMC 10B Problem 7 • 2015 AMC 10B Problem 21 • 2016 AMC 10A Problem 4 • 2016 AMC 10B Problem 25 • 2018 AMC 10A Problem 14 • 2018 AMC 10B Problem 25 • 2019 AMC 10B Problem 9 • 2020 AMC 10A Problem 22 • 2020 AMC 10B Problem 24 • 2021 AMC 10B Spring Problem 25 • 2021 AMC 10A Fall Problem 16 • 2023 AMC 10B Problem 22 • 2025 AMC 10B Problem 1 • 2025 AMC 10B Problem 18
AMC 12
1970 AMC 12 Problem 25 • 1973 AMC 12 Problem 30 • 1975 AMC 12 Problem 29 • 1977 AMC 12 Problem 11 • 1980 AMC 12 Problem 25 • 1982 AMC 12 Problem 15 • 1985 AMC 12 Problem 30 • 1989 AMC 12 Problem 20 • 2003 AMC 12B Problem 23 • 2004 AMC 12A Problem 2 • 2005 AMC 12A Problem 23 • 2006 AMC 12B Problem 20 • 2011 AMC 12A Problem 3 • 2011 AMC 12A Problem 19 • 2011 AMC 12B Problem 25 • 2012 AMC 12A Problem 25 • 2014 AMC 12A Problem 21 • 2015 AMC 12B Problem 21 • 2016 AMC 12A Problem 3 • 2016 AMC 12A Problem 25 • 2017 AMC 12B Problem 20 • 2018 AMC 12B Problem 24 • 2020 AMC 12A Problem 25 • 2020 AMC 12B Problem 21 • 2021 AMC 12B Spring Problem 25 • 2025 AMC 12B Problem 1
AIME
1985 AIME Problem 10 • 1991 AIME Problem 6 • 1994 AIME Problem 4 • 1994 AIME Problem 14 • 1995 AIME Problem 8 • 1996 AIME Problem 2 • 1997 AIME Problem 9 • 2002 AIME II Problem 8 • 2004 AIME I Problem 12 • 2007 AIME I Problem 5 • 2007 AIME I Problem 7 • 2007 AIME I Problem 11 • 2007 AIME II Problem 7 • 2008 AIME I Problem 12 • 2009 AIME I Problem 6 • 2010 AIME I Problem 8 • 2010 AIME I Problem 14 • 2011 AIME II Problem 15 • 2012 AIME II Problem 10 • 2015 AIME I Problem 14 • 2015 AIME II Problem 13 • 2017 AIME II Problem 13 • 2020 AIME II Problem 14 • 2022 AIME II Problem 8 • 2022 AIME II Problem 14 • 2023 AIME I Problem 10 • 2026 AIME II Problem 9