Putnam Practice Bank

492 problems · 1985–2025

Every problem from the William Lowell Putnam Competition since 1985, filterable by topic and difficulty. Each label links to that year's problems in Kiran Kedlaya's Putnam Archive; solutions are one click further. No statements or solutions are copied here.

Difficulty comes from position (1–2 entry, 3–4 middle, 5–6 hard), a rough guide only. Topics are from PutnamBench; problems it doesn't include are untagged. From 2026 the exam is four 90-minute sessions of three problems, so a good mock is three problems in 90 minutes.

• 1985 A1 sol entry · algebra
• 1985 A2 sol entry · untagged
• 1985 A3 sol middle · analysis
• 1985 A4 sol middle · number-theory
• 1985 A5 sol hard · analysis
• 1985 A6 sol hard · algebra
• 1985 B1 sol entry · algebra
• 1985 B2 sol entry · algebra
• 1985 B3 sol middle · algebra
• 1985 B4 sol middle · untagged
• 1985 B5 sol hard · analysis
• 1985 B6 sol hard · algebra
• 1986 A1 sol entry · analysis, algebra
• 1986 A2 sol entry · algebra
• 1986 A3 sol middle · analysis
• 1986 A4 sol middle · algebra
• 1986 A5 sol hard · analysis, algebra
• 1986 A6 sol hard · algebra
• 1986 B1 sol entry · algebra, geometry
• 1986 B2 sol entry · algebra
• 1986 B3 sol middle · number-theory, algebra
• 1986 B4 sol middle · analysis
• 1986 B5 sol hard · algebra
• 1986 B6 sol hard · algebra
• 1987 A1 sol entry · algebra
• 1987 A2 sol entry · algebra
• 1987 A3 sol middle · untagged
• 1987 A4 sol middle · algebra
• 1987 A5 sol hard · analysis
• 1987 A6 sol hard · analysis, algebra
• 1987 B1 sol entry · analysis
• 1987 B2 sol entry · algebra
• 1987 B3 sol middle · algebra
• 1987 B4 sol middle · analysis
• 1987 B5 sol hard · algebra
• 1987 B6 sol hard · algebra
• 1988 A1 sol entry · geometry
• 1988 A2 sol entry · analysis
• 1988 A3 sol middle · analysis
• 1988 A4 sol middle · combinatorics, geometry
• 1988 A5 sol hard · analysis
• 1988 A6 sol hard · algebra
• 1988 B1 sol entry · number-theory, algebra
• 1988 B2 sol entry · algebra
• 1988 B3 sol middle · algebra
• 1988 B4 sol middle · analysis
• 1988 B5 sol hard · algebra
• 1988 B6 sol hard · number-theory, algebra
• 1989 A1 sol entry · number-theory, algebra
• 1989 A2 sol entry · analysis
• 1989 A3 sol middle · algebra
• 1989 A4 sol middle · untagged
• 1989 A5 sol hard · untagged
• 1989 A6 sol hard · algebra
• 1989 B1 sol entry · geometry, probability
• 1989 B2 sol entry · algebra
• 1989 B3 sol middle · analysis
• 1989 B4 sol middle · combinatorics
• 1989 B5 sol hard · untagged
• 1989 B6 sol hard · analysis, algebra, probability
• 1990 A1 sol entry · algebra
• 1990 A2 sol entry · analysis
• 1990 A3 sol middle · untagged
• 1990 A4 sol middle · number-theory, combinatorics
• 1990 A5 sol hard · algebra
• 1990 A6 sol hard · algebra
• 1990 B1 sol entry · analysis
• 1990 B2 sol entry · analysis
• 1990 B3 sol middle · algebra
• 1990 B4 sol middle · algebra
• 1990 B5 sol hard · analysis, algebra
• 1990 B6 sol hard · untagged
• 1991 A1 sol entry · untagged
• 1991 A2 sol entry · algebra
• 1991 A3 sol middle · analysis, algebra
• 1991 A4 sol middle · analysis, geometry
• 1991 A5 sol hard · analysis
• 1991 A6 sol hard · algebra
• 1991 B1 sol entry · algebra
• 1991 B2 sol entry · analysis
• 1991 B3 sol middle · untagged
• 1991 B4 sol middle · number-theory, algebra
• 1991 B5 sol hard · number-theory
• 1991 B6 sol hard · analysis
• 1992 A1 sol entry · algebra
• 1992 A2 sol entry · analysis, algebra
• 1992 A3 sol middle · number-theory, algebra
• 1992 A4 sol middle · analysis
• 1992 A5 sol hard · algebra
• 1992 A6 sol hard · untagged
• 1992 B1 sol entry · algebra
• 1992 B2 sol entry · algebra
• 1992 B3 sol middle · analysis, geometry
• 1992 B4 sol middle · algebra
• 1992 B5 sol hard · analysis, algebra
• 1992 B6 sol hard · algebra
• 1993 A1 sol entry · analysis, algebra
• 1993 A2 sol entry · algebra
• 1993 A3 sol middle · algebra
• 1993 A4 sol middle · algebra
• 1993 A5 sol hard · analysis
• 1993 A6 sol hard · algebra
• 1993 B1 sol entry · algebra
• 1993 B2 sol entry · untagged
• 1993 B3 sol middle · number-theory, geometry, probability
• 1993 B4 sol middle · analysis
• 1993 B5 sol hard · number-theory, algebra, geometry
• 1993 B6 sol hard · algebra
• 1994 A1 sol entry · analysis
• 1994 A2 sol entry · untagged
• 1994 A3 sol middle · geometry
• 1994 A4 sol middle · algebra
• 1994 A5 sol hard · analysis
• 1994 A6 sol hard · algebra
• 1994 B1 sol entry · algebra
• 1994 B2 sol entry · algebra, geometry
• 1994 B3 sol middle · analysis
• 1994 B4 sol middle · number-theory, analysis, algebra
• 1994 B5 sol hard · algebra
• 1994 B6 sol hard · number-theory
• 1995 A1 sol entry · algebra
• 1995 A2 sol entry · analysis
• 1995 A3 sol middle · number-theory
• 1995 A4 sol middle · combinatorics
• 1995 A5 sol hard · analysis, algebra
• 1995 A6 sol hard · algebra
• 1995 B1 sol entry · combinatorics
• 1995 B2 sol entry · untagged
• 1995 B3 sol middle · algebra
• 1995 B4 sol middle · algebra
• 1995 B5 sol hard · untagged
• 1995 B6 sol hard · number-theory, algebra
• 1996 A1 sol entry · untagged
• 1996 A2 sol entry · geometry
• 1996 A3 sol middle · combinatorics
• 1996 A4 sol middle · algebra
• 1996 A5 sol hard · number-theory
• 1996 A6 sol hard · analysis, algebra
• 1996 B1 sol entry · algebra
• 1996 B2 sol entry · analysis
• 1996 B3 sol middle · algebra
• 1996 B4 sol middle · algebra
• 1996 B5 sol hard · algebra
• 1996 B6 sol hard · untagged
• 1997 A1 sol entry · geometry
• 1997 A2 sol entry · untagged
• 1997 A3 sol middle · analysis
• 1997 A4 sol middle · algebra
• 1997 A5 sol hard · number-theory
• 1997 A6 sol hard · algebra
• 1997 B1 sol entry · algebra
• 1997 B2 sol entry · analysis
• 1997 B3 sol middle · number-theory
• 1997 B4 sol middle · algebra
• 1997 B5 sol hard · number-theory
• 1997 B6 sol hard · untagged
• 1998 A1 sol entry · untagged
• 1998 A2 sol entry · geometry
• 1998 A3 sol middle · analysis
• 1998 A4 sol middle · algebra
• 1998 A5 sol hard · analysis
• 1998 A6 sol hard · geometry
• 1998 B1 sol entry · algebra
• 1998 B2 sol entry · algebra, geometry
• 1998 B3 sol middle · untagged
• 1998 B4 sol middle · number-theory
• 1998 B5 sol hard · number-theory
• 1998 B6 sol hard · number-theory
• 1999 A1 sol entry · algebra
• 1999 A2 sol entry · algebra
• 1999 A3 sol middle · algebra
• 1999 A4 sol middle · number-theory
• 1999 A5 sol hard · analysis
• 1999 A6 sol hard · algebra
• 1999 B1 sol entry · untagged
• 1999 B2 sol entry · analysis
• 1999 B3 sol middle · algebra
• 1999 B4 sol middle · analysis
• 1999 B5 sol hard · algebra
• 1999 B6 sol hard · number-theory
• 2000 A1 sol entry · analysis
• 2000 A2 sol entry · number-theory
• 2000 A3 sol middle · untagged
• 2000 A4 sol middle · analysis
• 2000 A5 sol hard · algebra
• 2000 A6 sol hard · algebra
• 2000 B1 sol entry · algebra
• 2000 B2 sol entry · number-theory, algebra
• 2000 B3 sol middle · analysis
• 2000 B4 sol middle · analysis
• 2000 B5 sol hard · algebra
• 2000 B6 sol hard · untagged
• 2001 A1 sol entry · algebra
• 2001 A2 sol entry · untagged
• 2001 A3 sol middle · algebra
• 2001 A4 sol middle · untagged
• 2001 A5 sol hard · number-theory
• 2001 A6 sol hard · untagged
• 2001 B1 sol entry · algebra
• 2001 B2 sol entry · algebra
• 2001 B3 sol middle · analysis
• 2001 B4 sol middle · algebra
• 2001 B5 sol hard · analysis
• 2001 B6 sol hard · analysis
• 2002 A1 sol entry · analysis, algebra
• 2002 A2 sol entry · geometry
• 2002 A3 sol middle · algebra
• 2002 A4 sol middle · untagged
• 2002 A5 sol hard · number-theory, algebra
• 2002 A6 sol hard · number-theory, analysis
• 2002 B1 sol entry · untagged
• 2002 B2 sol entry · untagged
• 2002 B3 sol middle · algebra
• 2002 B4 sol middle · untagged
• 2002 B5 sol hard · number-theory
• 2002 B6 sol hard · number-theory, algebra
• 2003 A1 sol entry · algebra
• 2003 A2 sol entry · algebra
• 2003 A3 sol middle · analysis
• 2003 A4 sol middle · algebra
• 2003 A5 sol hard · combinatorics
• 2003 A6 sol hard · algebra
• 2003 B1 sol entry · algebra
• 2003 B2 sol entry · algebra
• 2003 B3 sol middle · number-theory
• 2003 B4 sol middle · number-theory, algebra
• 2003 B5 sol hard · geometry
• 2003 B6 sol hard · analysis
• 2004 A1 sol entry · probability
• 2004 A2 sol entry · untagged
• 2004 A3 sol middle · algebra
• 2004 A4 sol middle · algebra
• 2004 A5 sol hard · combinatorics
• 2004 A6 sol hard · analysis
• 2004 B1 sol entry · algebra
• 2004 B2 sol entry · algebra
• 2004 B3 sol middle · untagged
• 2004 B4 sol middle · geometry
• 2004 B5 sol hard · analysis
• 2004 B6 sol hard · analysis
• 2005 A1 sol entry · number-theory
• 2005 A2 sol entry · combinatorics
• 2005 A3 sol middle · analysis, algebra
• 2005 A4 sol middle · algebra
• 2005 A5 sol hard · analysis
• 2005 A6 sol hard · untagged
• 2005 B1 sol entry · algebra
• 2005 B2 sol entry · algebra
• 2005 B3 sol middle · analysis
• 2005 B4 sol middle · algebra
• 2005 B5 sol hard · algebra
• 2005 B6 sol hard · algebra
• 2006 A1 sol entry · geometry
• 2006 A2 sol entry · untagged
• 2006 A3 sol middle · algebra
• 2006 A4 sol middle · algebra
• 2006 A5 sol hard · algebra
• 2006 A6 sol hard · untagged
• 2006 B1 sol entry · geometry
• 2006 B2 sol entry · analysis
• 2006 B3 sol middle · geometry
• 2006 B4 sol middle · algebra
• 2006 B5 sol hard · analysis, algebra
• 2006 B6 sol hard · analysis
• 2007 A1 sol entry · algebra, geometry
• 2007 A2 sol entry · geometry
• 2007 A3 sol middle · combinatorics
• 2007 A4 sol middle · number-theory, analysis, algebra
• 2007 A5 sol hard · algebra
• 2007 A6 sol hard · untagged
• 2007 B1 sol entry · algebra
• 2007 B2 sol entry · analysis
• 2007 B3 sol middle · analysis
• 2007 B4 sol middle · algebra
• 2007 B5 sol hard · algebra
• 2007 B6 sol hard · analysis, combinatorics
• 2008 A1 sol entry · algebra
• 2008 A2 sol entry · untagged
• 2008 A3 sol middle · number-theory
• 2008 A4 sol middle · algebra
• 2008 A5 sol hard · algebra, geometry
• 2008 A6 sol hard · algebra
• 2008 B1 sol entry · number-theory, geometry
• 2008 B2 sol entry · analysis
• 2008 B3 sol middle · geometry
• 2008 B4 sol middle · number-theory, algebra
• 2008 B5 sol hard · analysis
• 2008 B6 sol hard · number-theory
• 2009 A1 sol entry · algebra, geometry
• 2009 A2 sol entry · analysis
• 2009 A3 sol middle · analysis, algebra
• 2009 A4 sol middle · number-theory
• 2009 A5 sol hard · algebra
• 2009 A6 sol hard · untagged
• 2009 B1 sol entry · number-theory
• 2009 B2 sol entry · analysis, algebra
• 2009 B3 sol middle · number-theory
• 2009 B4 sol middle · algebra
• 2009 B5 sol hard · analysis
• 2009 B6 sol hard · number-theory
• 2010 A1 sol entry · algebra
• 2010 A2 sol entry · analysis
• 2010 A3 sol middle · analysis
• 2010 A4 sol middle · number-theory
• 2010 A5 sol hard · algebra
• 2010 A6 sol hard · analysis
• 2010 B1 sol entry · analysis
• 2010 B2 sol entry · geometry
• 2010 B3 sol middle · analysis
• 2010 B4 sol middle · algebra
• 2010 B5 sol hard · analysis
• 2010 B6 sol hard · algebra
• 2011 A1 sol entry · algebra, geometry
• 2011 A2 sol entry · analysis
• 2011 A3 sol middle · analysis
• 2011 A4 sol middle · algebra
• 2011 A5 sol hard · analysis
• 2011 A6 sol hard · algebra
• 2011 B1 sol entry · algebra
• 2011 B2 sol entry · number-theory
• 2011 B3 sol middle · analysis
• 2011 B4 sol middle · algebra
• 2011 B5 sol hard · analysis
• 2011 B6 sol hard · number-theory
• 2012 A1 sol entry · algebra, geometry
• 2012 A2 sol entry · algebra
• 2012 A3 sol middle · analysis, algebra
• 2012 A4 sol middle · algebra
• 2012 A5 sol hard · algebra
• 2012 A6 sol hard · analysis
• 2012 B1 sol entry · algebra
• 2012 B2 sol entry · untagged
• 2012 B3 sol middle · combinatorics
• 2012 B4 sol middle · analysis
• 2012 B5 sol hard · analysis
• 2012 B6 sol hard · number-theory
• 2013 A1 sol entry · untagged
• 2013 A2 sol entry · number-theory, algebra
• 2013 A3 sol middle · analysis
• 2013 A4 sol middle · algebra
• 2013 A5 sol hard · algebra, geometry
• 2013 A6 sol hard · algebra
• 2013 B1 sol entry · algebra
• 2013 B2 sol entry · algebra
• 2013 B3 sol middle · combinatorics
• 2013 B4 sol middle · analysis
• 2013 B5 sol hard · algebra
• 2013 B6 sol hard · untagged
• 2014 A1 sol entry · number-theory, analysis
• 2014 A2 sol entry · algebra
• 2014 A3 sol middle · algebra
• 2014 A4 sol middle · analysis, probability
• 2014 A5 sol hard · algebra
• 2014 A6 sol hard · algebra
• 2014 B1 sol entry · algebra
• 2014 B2 sol entry · analysis
• 2014 B3 sol middle · number-theory, algebra
• 2014 B4 sol middle · algebra
• 2014 B5 sol hard · untagged
• 2014 B6 sol hard · number-theory, analysis
• 2015 A1 sol entry · analysis, geometry
• 2015 A2 sol entry · number-theory
• 2015 A3 sol middle · number-theory, algebra
• 2015 A4 sol middle · analysis
• 2015 A5 sol hard · number-theory
• 2015 A6 sol hard · algebra
• 2015 B1 sol entry · analysis
• 2015 B2 sol entry · number-theory
• 2015 B3 sol middle · algebra
• 2015 B4 sol middle · algebra
• 2015 B5 sol hard · algebra
• 2015 B6 sol hard · number-theory, analysis
• 2016 A1 sol entry · number-theory, algebra
• 2016 A2 sol entry · analysis
• 2016 A3 sol middle · analysis
• 2016 A4 sol middle · untagged
• 2016 A5 sol hard · algebra
• 2016 A6 sol hard · algebra
• 2016 B1 sol entry · analysis
• 2016 B2 sol entry · analysis
• 2016 B3 sol middle · geometry
• 2016 B4 sol middle · algebra, probability
• 2016 B5 sol hard · algebra
• 2016 B6 sol hard · analysis
• 2017 A1 sol entry · number-theory
• 2017 A2 sol entry · algebra
• 2017 A3 sol middle · analysis
• 2017 A4 sol middle · algebra
• 2017 A5 sol hard · untagged
• 2017 A6 sol hard · untagged
• 2017 B1 sol entry · geometry
• 2017 B2 sol entry · algebra
• 2017 B3 sol middle · number-theory
• 2017 B4 sol middle · algebra
• 2017 B5 sol hard · untagged
• 2017 B6 sol hard · number-theory, algebra
• 2018 A1 sol entry · number-theory
• 2018 A2 sol entry · algebra
• 2018 A3 sol middle · number-theory
• 2018 A4 sol middle · number-theory, algebra
• 2018 A5 sol hard · analysis
• 2018 A6 sol hard · algebra, geometry
• 2018 B1 sol entry · algebra
• 2018 B2 sol entry · analysis
• 2018 B3 sol middle · number-theory
• 2018 B4 sol middle · algebra
• 2018 B5 sol hard · analysis
• 2018 B6 sol hard · algebra
• 2019 A1 sol entry · algebra
• 2019 A2 sol entry · untagged
• 2019 A3 sol middle · algebra
• 2019 A4 sol middle · analysis
• 2019 A5 sol hard · number-theory, algebra
• 2019 A6 sol hard · analysis
• 2019 B1 sol entry · geometry
• 2019 B2 sol entry · analysis
• 2019 B3 sol middle · algebra
• 2019 B4 sol middle · analysis
• 2019 B5 sol hard · number-theory, algebra
• 2019 B6 sol hard · algebra
• 2020 A1 sol entry · number-theory, algebra
• 2020 A2 sol entry · algebra
• 2020 A3 sol middle · analysis
• 2020 A4 sol middle · untagged
• 2020 A5 sol hard · number-theory, combinatorics
• 2020 A6 sol hard · algebra
• 2020 B1 sol entry · algebra
• 2020 B2 sol entry · untagged
• 2020 B3 sol middle · untagged
• 2020 B4 sol middle · algebra
• 2020 B5 sol hard · algebra
• 2020 B6 sol hard · algebra
• 2021 A1 sol entry · geometry
• 2021 A2 sol entry · analysis
• 2021 A3 sol middle · geometry
• 2021 A4 sol middle · analysis
• 2021 A5 sol hard · number-theory
• 2021 A6 sol hard · number-theory, algebra
• 2021 B1 sol entry · untagged
• 2021 B2 sol entry · analysis
• 2021 B3 sol middle · analysis
• 2021 B4 sol middle · number-theory
• 2021 B5 sol hard · number-theory, algebra
• 2021 B6 sol hard · untagged
• 2022 A1 sol entry · algebra
• 2022 A2 sol entry · algebra
• 2022 A3 sol middle · number-theory
• 2022 A4 sol middle · probability
• 2022 A5 sol hard · combinatorics
• 2022 A6 sol hard · algebra
• 2022 B1 sol entry · analysis, algebra
• 2022 B2 sol entry · algebra
• 2022 B3 sol middle · algebra
• 2022 B4 sol middle · algebra
• 2022 B5 sol hard · algebra, probability
• 2022 B6 sol hard · analysis
• 2023 A1 sol entry · analysis
• 2023 A2 sol entry · algebra
• 2023 A3 sol middle · analysis
• 2023 A4 sol middle · number-theory, geometry
• 2023 A5 sol hard · algebra
• 2023 A6 sol hard · combinatorics
• 2023 B1 sol entry · combinatorics
• 2023 B2 sol entry · number-theory
• 2023 B3 sol middle · combinatorics, probability
• 2023 B4 sol middle · analysis
• 2023 B5 sol hard · number-theory
• 2023 B6 sol hard · algebra
• 2024 A1 sol entry · number-theory
• 2024 A2 sol entry · algebra
• 2024 A3 sol middle · combinatorics
• 2024 A4 sol middle · number-theory
• 2024 A5 sol hard · geometry, probability
• 2024 A6 sol hard · algebra
• 2024 B1 sol entry · combinatorics
• 2024 B2 sol entry · untagged
• 2024 B3 sol middle · analysis
• 2024 B4 sol middle · probability
• 2024 B5 sol hard · algebra, combinatorics
• 2024 B6 sol hard · analysis
• 2025 A1 sol entry · number-theory
• 2025 A2 sol entry · analysis
• 2025 A3 sol middle · combinatorics
• 2025 A4 sol middle · algebra
• 2025 A5 sol hard · combinatorics
• 2025 A6 sol hard · number-theory
• 2025 B1 sol entry · combinatorics, geometry
• 2025 B2 sol entry · analysis, geometry
• 2025 B3 sol middle · number-theory
• 2025 B4 sol middle · algebra, combinatorics
• 2025 B5 sol hard · number-theory
• 2025 B6 sol hard · number-theory, analysis