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 of these problems are used with official legal permission of the Mathematical Association of America (MAA).
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
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
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