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==AOPS Contributions== | ==AOPS Contributions== | ||
| + | |||
| + | === AJHSME === | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1994_AJHSME_Problems/Problem_25#Solution_2 1994 AJHSME Problem 25 Solution 2] (Number Theory) | ||
=== AHSME === | === AHSME === | ||
| − | + | # [https://artofproblemsolving.com/wiki/index.php/1991_AHSME_Problems/Problem_30#Solution_2_.28PIE.29 1991 AHSME Problem 30 Solution 2] (Combinatorics) | |
| − | # [https://artofproblemsolving.com/wiki/index.php/1995_AHSME_Problems/Problem_27# | + | # [https://artofproblemsolving.com/wiki/index.php/1994_AHSME_Problems/Problem_28#Solution_2 1994 AHSME Problem 28 Solution 2] (Analytic Geometry) |
| + | # [https://artofproblemsolving.com/wiki/index.php/1994_AHSME_Problems/Problem_29#Solution_2 1994 AHSME Problem 29 Solution 2] (Geometry, Trigonometry) | ||
| + | # [https://artofproblemsolving.com/wiki/index.php/1995_AHSME_Problems/Problem_30#Solution_2 1995 AHSME Problem 30 Solution 2] (3D Geometry) | ||
| + | # [https://artofproblemsolving.com/wiki/index.php/1996_AHSME_Problems/Problem_27#Solution_3 1996 AHSME Problem 27 Solution 3] (3D Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1996_AHSME_Problems/Problem_30#Solution_4 1996 AHSME Problem 30 Solution 4] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1996_AHSME_Problems/Problem_30#Solution_5 1996 AHSME Problem 30 Solution 5] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1996_AHSME_Problems/Problem_30#Solution_6_.28Ptolemy.27s_theorem.29 1996 AHSME Problem 30 Solution 6] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1997_AHSME_Problems/Problem_30#Solution_3_.28Casework.29 1997 AHSME Problem 30 Solution 3] (Combinatorics) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1998_AHSME_Problems/Problem_28#Solution_4 1998 AHSME Problem 28 Solution 4] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1999_AHSME_Problems/Problem_25#Solution_4 1999 AHSME Problem 25 Solution 4] (Number Theory) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1999_AHSME_Problems/Problem_27#Supplement 1999 AHSME Problem 27 Supplement] (Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1999_AHSME_Problems/Problem_28#Solution_2 1999 AHSME Problem 28 Solution 2] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/1999_AHSME_Problems/Problem_29#Solution_2 1999 AHSME Problem 29 Solution 2] (3D Geometry) | ||
=== AMC 8 === | === AMC 8 === | ||
| − | + | #[https://artofproblemsolving.com/wiki/index.php/2004_AMC_8_Problems/Problem_14#Solution_1 2004 AMC8 Problem 14 Solution 1] (Geometry) | |
# [https://artofproblemsolving.com/wiki/index.php/2022_AMC_8_Problems/Problem_25#Solution_4_.28Dynamic_Programming.29 2022 AMC8 Problem 25 Solution 4] (Probability) | # [https://artofproblemsolving.com/wiki/index.php/2022_AMC_8_Problems/Problem_25#Solution_4_.28Dynamic_Programming.29 2022 AMC8 Problem 25 Solution 4] (Probability) | ||
# [https://artofproblemsolving.com/wiki/index.php/2022_AMC_8_Problems/Problem_25#Remark 2022 AMC8 Problem 25 Remark] (Probability) | # [https://artofproblemsolving.com/wiki/index.php/2022_AMC_8_Problems/Problem_25#Remark 2022 AMC8 Problem 25 Remark] (Probability) | ||
| Line 23: | Line 38: | ||
# [https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_Problems/Problem_24#Solution_3 2015 AMC10A Problem 24 Solution 3] (Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2015_AMC_10A_Problems/Problem_24#Solution_3 2015 AMC10A Problem 24 Solution 3] (Geometry) | ||
# [https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_19#Solution_3 2015 AMC10B Problem 19 Solution 3] (Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2015_AMC_10B_Problems/Problem_19#Solution_3 2015 AMC10B Problem 19 Solution 3] (Geometry) | ||
| − | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_20# | + | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_20#Solution_3_.28Casework.29 2016 AMC10A Problem 20 Solution 3] (Combinatorics) |
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_19#Solution_4_.28Area.29 2016 AMC10B Problem 19 Solution 4] (Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_19#Solution_4_.28Area.29 2016 AMC10B Problem 19 Solution 4] (Geometry) | ||
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_19#Solution_5_.28Area.29 2016 AMC10B Problem 19 Solution 5] (Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_19#Solution_5_.28Area.29 2016 AMC10B Problem 19 Solution 5] (Geometry) | ||
| Line 29: | Line 44: | ||
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Supplement 2016 AMC10B Problem 25 Solution 1 Supplement] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Supplement 2016 AMC10B Problem 25 Solution 1 Supplement] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Solution_3_.28Casework.29 2016 AMC10B Problem 25 Solution 3] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Solution_3_.28Casework.29 2016 AMC10B Problem 25 Solution 3] (Number Theory) | ||
| + | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Solution_4 2016 AMC10B Problem 25 Solution 4] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Remark 2016 AMC10B Problem 25 Remark] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10B_Problems/Problem_25#Remark 2016 AMC10B Problem 25 Remark] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2017_AMC_10B_Problems/Problem_17#Solution_4 2017 AMC10B Problem 17 Solution 4] (Combinatorics) | # [https://artofproblemsolving.com/wiki/index.php/2017_AMC_10B_Problems/Problem_17#Solution_4 2017 AMC10B Problem 17 Solution 4] (Combinatorics) | ||
| Line 41: | Line 57: | ||
# [https://artofproblemsolving.com/wiki/index.php/2019_AMC_10B_Problems/Problem_22#Solution_4_.28Markov_Chain.29 2019 AMC10B Problem 22 Solution 4] (Probability, Markov Chain) | # [https://artofproblemsolving.com/wiki/index.php/2019_AMC_10B_Problems/Problem_22#Solution_4_.28Markov_Chain.29 2019 AMC10B Problem 22 Solution 4] (Probability, Markov Chain) | ||
# [https://artofproblemsolving.com/wiki/index.php/2019_AMC_10B_Problems/Problem_25#Solution_6_.28Recursion.29 2019 AMC10B Problem 25 Solution 6] (Combinatorics) | # [https://artofproblemsolving.com/wiki/index.php/2019_AMC_10B_Problems/Problem_25#Solution_6_.28Recursion.29 2019 AMC10B Problem 25 Solution 6] (Combinatorics) | ||
| − | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_20# | + | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_20#Solution_7_.28Solving_Equations.29 2020 AMC10A Problem 20 Solution 7] (Geometry) |
# [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_24#Solution_9_.28Euclidean_Algorithm.29 2020 AMC10A Problem 24 Solution 9] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_24#Solution_9_.28Euclidean_Algorithm.29 2020 AMC10A Problem 24 Solution 9] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_24#Solution_10_.28Diophantine_Equations.29 2020 AMC10A Problem 24 Solution 10] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_24#Solution_10_.28Diophantine_Equations.29 2020 AMC10A Problem 24 Solution 10] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_24#Solution_11_.28Chinese_Remainder_Theorem.29 2020 AMC10A Problem 24 Solution 11] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10A_Problems/Problem_24#Solution_11_.28Chinese_Remainder_Theorem.29 2020 AMC10A Problem 24 Solution 11] (Number Theory) | ||
| − | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_13#Solution_3_. | + | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_13#Solution_3_.28Pattern.29 2020 AMC10B Problem 13 Solution 3] (Combinatorics) |
# [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_21#Solution_6 2020 AMC10B Problem 21 Solution 6] (Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_21#Solution_6 2020 AMC10B Problem 21 Solution 6] (Geometry) | ||
| − | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_23# | + | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_23#Solution_5_.28Group_Theory.29 2020 AMC10B Problem 23 Solution 5] (Group Theory) |
| − | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_24# | + | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_24#Solution_8 2020 AMC10B Problem 24 Solution 8] (Algebra) |
# [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_25#Solution_7_.28Integer_Partition.29 2020 AMC10B Problem 25 Solution 7] (Combinatorics) | # [https://artofproblemsolving.com/wiki/index.php/2020_AMC_10B_Problems/Problem_25#Solution_7_.28Integer_Partition.29 2020 AMC10B Problem 25 Solution 7] (Combinatorics) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_AMC_12A_Problems/Problem_23#Solution_8_.28Markov_Chain.29 2021 Spring AMC10A Problem 23 Solution 8] (Probability, Markov Chain) | # [https://artofproblemsolving.com/wiki/index.php/2021_AMC_12A_Problems/Problem_23#Solution_8_.28Markov_Chain.29 2021 Spring AMC10A Problem 23 Solution 8] (Probability, Markov Chain) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_AMC_10A_Problems/Problem_24#Solution_3_.28Slopes_and_Intercepts.29 2021 Spring AMC10A Problem 24 Solution 3] (Analytic Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2021_AMC_10A_Problems/Problem_24#Solution_3_.28Slopes_and_Intercepts.29 2021 Spring AMC10A Problem 24 Solution 3] (Analytic Geometry) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_AMC_10A_Problems/Problem_25#Solution_4_.28Casework_and_Symmetry.29 2021 Spring AMC10A Problem 25 Solution 4] (Combinatorics) | # [https://artofproblemsolving.com/wiki/index.php/2021_AMC_10A_Problems/Problem_25#Solution_4_.28Casework_and_Symmetry.29 2021 Spring AMC10A Problem 25 Solution 4] (Combinatorics) | ||
| + | # [https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_25#Solution_4 2021 Spring AMC10B Problem 25 Solution 4] (Analytic Geometry) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_25#Solution_5 2021 Spring AMC10B Problem 25 Solution 5] (Analytic Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_25#Solution_5 2021 Spring AMC10B Problem 25 Solution 5] (Analytic Geometry) | ||
| + | # [https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_25#Remark 2021 Spring AMC10B Problem 25 Remark] (Analytic Geometry) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_10A_Problems/Problem_24#Solution_4 2021 Fall AMC10A Problem 24 Solution 4] (Graph Theory) | # [https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_10A_Problems/Problem_24#Solution_4 2021 Fall AMC10A Problem 24 Solution 4] (Graph Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_12B_Problems/Problem_7#Solution_1_.28Completing_the_Square.29 2021 Fall AMC10B Problem 12 Solution 1] (Algebra) | # [https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_12B_Problems/Problem_7#Solution_1_.28Completing_the_Square.29 2021 Fall AMC10B Problem 12 Solution 1] (Algebra) | ||
| Line 62: | Line 80: | ||
===AMC 12=== | ===AMC 12=== | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2000_AMC_12_Problems/Problem_25#Solution_5_.28Graph_Theory.29 2000 AMC12 Problem 25 Solution 5] (Graph Theory) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2001_AMC_12_Problems/Problem_22#Solution_5 2001 AMC12 Problem 22 Solution 5] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2001_AMC_12_Problems/Problem_24#Solution_5_.28Law_of_Sines.29 2001 AMC12 Problem 24 Solution 5] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2002_AMC_12A_Problems/Problem_23#Solution_4 2002 AMC12A Problem 23 Solution 4] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2002_AMC_12A_Problems/Problem_23#Solution_5_.28Trigonometry.29 2002 AMC12A Problem 23 Solution 5] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2003_AMC_12A_Problems/Problem_17#Solution_8 2003 AMC12A Problem 17 Solution 8] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2003_AMC_12B_Problems/Problem_21#Solution_2_.28Analytic_Geometry.29 2003 AMC12B Problem 21 Solution 2] (Analytic Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2003_AMC_12B_Problems/Problem_25#Solution_3 2003 AMC12B Problem 25 Solution 3] (Probability) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2007_AMC_12B_Problems/Problem_23#Solution_3 2007 AMC12B Problem 23 Solution 3] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2009_AMC_12B_Problems/Problem_24#Solution_4 2009 AMC12B Problem 24 Solution 4] (Trigonometry) | ||
#[https://artofproblemsolving.com/wiki/index.php/2010_AMC_12A_Problems/Problem_23#Remark_.28Chinese_Remainder_Theorem.29 2010 AMC12A Problem 23 Remark] (Number Theory) | #[https://artofproblemsolving.com/wiki/index.php/2010_AMC_12A_Problems/Problem_23#Remark_.28Chinese_Remainder_Theorem.29 2010 AMC12A Problem 23 Remark] (Number Theory) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2010_AMC_12B_Problems/Problem_23#Solution_4 2010 AMC12B Problem 23 Solution 4] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2011_AMC_12B_Problems/Problem_20#Solution_6_.28Trigonometry.29 2011 AMC12B Problem 20 Solution 6] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2012_AMC_12B_Problems/Problem_17#Solution_6 2012 AMC12B Problem 17 Solution 6] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2012_AMC_12B_Problems/Problem_18#Solution_5_.28Recursion.29 2012 AMC12B Problem 18 Solution 5] (Combinatorics) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2012_AMC_12B_Problems/Problem_19#Solution_3 2012 AMC12B Problem 19 Solution 3] (3D Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2012_AMC_12B_Problems/Problem_20#Solution_2 2012 AMC12B Problem 20 Solution 2] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2012_AMC_12B_Problems/Problem_21#Solution_4 2012 AMC12B Problem 21 Solution 4] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2013_AMC_12A_Problems/Problem_16#Solution_4 2013 AMC12A Problem 16 Solution 4] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2013_AMC_12A_Problems/Problem_18#Solution_3_.28Simply_Drawing.29 2013 AMC12A Problem 18 Solution 3] (3D Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2013_AMC_12B_Problems/Problem_24#Solution_6 2013 AMC12B Problem 24 Solution 6] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2013_AMC_12B_Problems/Problem_25#Solution_3 2013 AMC12B Problem 25 Solution 3] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2014_AMC_12A_Problems/Problem_20#Remark 2014 AMC12A Problem 20 Remark] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2014_AMC_10A_Problems/Problem_25#Solution_2 2014 AMC12A Problem 22 Solution 2] (Number Theory) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2014_AMC_12B_Problems/Problem_21#Solution_6 2014 AMC12B Problem 21 Solution 6] (Geometry) | ||
#[https://artofproblemsolving.com/wiki/index.php/2014_AMC_12B_Problems/Problem_22#Remark_.28Markov_Chain.29 2014 AMC12B Problem 22 Remark] (Probability, Markov Chain) | #[https://artofproblemsolving.com/wiki/index.php/2014_AMC_12B_Problems/Problem_22#Remark_.28Markov_Chain.29 2014 AMC12B Problem 22 Remark] (Probability, Markov Chain) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2014_AMC_12B_Problems/Problem_24#Solution_4 2014 AMC12B Problem 24 Solution 4] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_23#Solution_5 2016 AMC12A Problem 20 Solution 5] (Algebra) | ||
# [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_24#Remark_.28Morley.27s_Trisector_Theorem.29 2016 AMC12A Problem 21 Remark] (Geometry) | # [https://artofproblemsolving.com/wiki/index.php/2016_AMC_10A_Problems/Problem_24#Remark_.28Morley.27s_Trisector_Theorem.29 2016 AMC12A Problem 21 Remark] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2016_AMC_12B_Problems/Problem_15#Solution_4 2016 AMC12B Problem 15 Solution 4] (Combinatorics) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2017_AMC_12A_Problems/Problem_22#Remark_.28Markov_Chain.29 2017 AMC12A Problem 22 Remark] (Probability, Markov Chain) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2017_AMC_12A_Problems/Problem_24#Solution_4 2017 AMC12A Problem 24 Solution 4] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2017_AMC_12A_Problems/Problem_25#Solution_6_.28Casework.29 2017 AMC12A Problem 25 Solution 6] (Algebra & Probability) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2017_AMC_12B_Problems/Problem_22#Solution_5_.28Casework.29 2017 AMC12B Problem 22 Solution 5] (Probability) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2017_AMC_12B_Problems/Problem_24#Solution_3 2017 AMC12B Problem 24 Solution 3] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2018_AMC_12A_Problems/Problem_21#Solution_4 2018 AMC12A Problem 21 Solution 4] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2018_AMC_12A_Problems/Problem_21#Solution_5_.28Monotonic_Function.29 2018 AMC12A Problem 21 Solution 5] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2018_AMC_12A_Problems/Problem_21#Solution_6_.28Proof_by_Contradiction.29 2018 AMC12A Problem 21 Solution 6] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2018_AMC_12B_Problems/Problem_25#Solution_6_.28Trignometry_Bash.29 2018 AMC12B Problem 25 Solution 6] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2019_AMC_10A_Problems/Problem_22#Solution_4 2019 AMC12A Problem 20 Solution 4] (Probability) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2020_AMC_12A_Problems/Problem_24#Solution_9_.28Trig_Bash.29 2020 AMC12A Problem 24 Solution 9] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2020_AMC_12B_Problems/Problem_25#Solution_2_.28Trigonometry_Identities.29 2020 AMC12B Problem 25 Solution 2] (Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2020_AMC_12B_Problems/Problem_25#Solution_4_.28Calculus_Finish.29 2020 AMC12B Problem 25 Solution 4] (Calculus) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_AMC_12A_Problems/Problem_24#Solution_5_.28Law_of_Sine_and_Power_of_a_Point.29 2021 Spring AMC12A Problem 24 Solution 5] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_18#Solution_2 2021 Spring AMC12B Problem 18 Solution 2] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_20#Solution_7_.28Factorization.29 2021 Spring AMC12B Problem 20 Solution 7] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_AMC_12B_Problems/Problem_24#Solution_6_.28Similar_Triangles_.26_Pythagorean_Theorem.29 2021 Spring AMC12B Problem 24 Solution 6] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_Fall_AMC_12B_Problems/Problem_24#Solution_1_.28Reflection.29 2021 Fall AMC12B Problem 24 Solution 1] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2022_AMC_10A_Problems/Problem_23#Solution_5_.28Polar_Coordinates.29 2022 AMC12A Problem 20 Solution 5] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_22#Solution_5_.28Calculus_Finish.29 2022 AMC12A Problem 23 Solution 5] (Calculus) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2022_AMC_12A_Problems/Problem_25#Solution_3 2022 AMC12A Problem 25 Solution 3] (Geometry, Number Theory) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_19#Solution_3_.28Law_of_Cosine.29 2022 AMC12B Problem 19 Solution 3] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_24#Supplement_.28Explanation_of_why_cos.282.CF.80.2F7.29_.2B_cos.284.CF.80.2F7.29_.2B_cos.286.CF.80.2F7.29_.3D_-1.2F2.29 2022 AMC12B Problem 24 Supplement] (Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_25#Solution_3_.28Euclidean_Geometry.29 2022 AMC12B Problem 25 Solution 3] (Geometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_20#Solution_3_.28Recursion.29 2023 AMC12A Problem 20 Solution 3] (Combinatorics) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_21#Solution_6_.28Case_Work.29 2023 AMC12A Problem 21 Solution 6] (Probability) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12A_Problems/Problem_25#Solution_1 2023 AMC12A Problem 25 Solution 1] (Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_16#Solution_3_.28Modulo_6.29 2023 AMC12B Problem 16 Solution 3] (Number Theory) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_17#Solution_2 2023 AMC12B Problem 17 Solution 2] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_17#Solution_3 2023 AMC12B Problem 17 Solution 3] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_18#Solution_3_.28Algebra.29 2023 AMC12B Problem 18 Solution 3] (Algebra) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_20#Solution_1 2023 AMC12B Problem 20 Solution 1] (Geometry, Trigonometry) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_25#Supplement_.28Calculating_sin54.2Fcos36_from_Scratch.29 2023 AMC12B Problem 25 Supplement] (Geometry, Trigonometry) | ||
===AIME=== | ===AIME=== | ||
| − | # 1983 AIME Problem 4 Solution | + | # [https://artofproblemsolving.com/wiki/index.php/1983_AIME_Problems/Problem_4#Solution_6_.28Trigonometry.29 1983 AIME Problem 4 Solution 6] (Geometry, Trigonometry) |
| + | # [https://artofproblemsolving.com/wiki/index.php/1983_AIME_Problems/Problem_7#Solution_7 1983 AIME Problem 7 Solution 7] (Combinatorics) | ||
# [https://artofproblemsolving.com/wiki/index.php/1985_AIME_Problems/Problem_12#Solution_5_.28Dynamic_Programming.29 1985 AIME Problem 12 Solution 5] (Probability) | # [https://artofproblemsolving.com/wiki/index.php/1985_AIME_Problems/Problem_12#Solution_5_.28Dynamic_Programming.29 1985 AIME Problem 12 Solution 5] (Probability) | ||
| − | #[https://artofproblemsolving.com/wiki/index.php/2021_AIME_I_Problems/Problem_12# | + | # [https://artofproblemsolving.com/wiki/index.php/1997_AIME_Problems/Problem_9#Solution_4 1997 AIME Problem 9 Solution 4] (Algebra) |
| + | #[https://artofproblemsolving.com/wiki/index.php/2001_AIME_II_Problems/Problem_9#Solution_3_.28Case_Work.29 2001 AIME II Problem 9 Solution 3] (Combinatorics) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_AIME_I_Problems/Problem_12#Solution_2_.28Markov_Chain.29 2021 AIME I Problem 12 Solution 2] (Probability, Markov Chain) | ||
| + | #[https://artofproblemsolving.com/wiki/index.php/2021_AIME_I_Problems/Problem_12#Remark_.28Markov_Chain.29 2021 AIME I Problem 12 Remark] (Probability, Markov Chain) | ||
# [https://artofproblemsolving.com/wiki/index.php/2021_AIME_II_Problems/Problem_8#Solution_2_.28Markov_Chain_and_Dynamic_Programming.29 2021 AIME II Problem 8 Solution 2] (Probability, Markov Chain) | # [https://artofproblemsolving.com/wiki/index.php/2021_AIME_II_Problems/Problem_8#Solution_2_.28Markov_Chain_and_Dynamic_Programming.29 2021 AIME II Problem 8 Solution 2] (Probability, Markov Chain) | ||
| − | # [https://artofproblemsolving.com/wiki/index.php/2021_AIME_II_Problems/Problem_8# | + | # [https://artofproblemsolving.com/wiki/index.php/2021_AIME_II_Problems/Problem_8#Remark_.28Markov_Chain.29 2021 AIME II Problem 8 Remark] (Probability, Markov Chain) |
| − | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_I_Problems/Problem_8#Solution_2_. | + | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_I_Problems/Problem_8#Solution_2_.28Euclidean_Geometry.29 2022 AIME I Problem 8 Solution 2] (Geometry) |
| − | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_2# | + | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_2#Solution 2022 AIME II Problem 2 Solution] (Probability) |
# [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_5#Solution_1 2022 AIME II Problem 5 Solution 1] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_5#Solution_1 2022 AIME II Problem 5 Solution 1] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_6#Solution_1 2022 AIME II Problem 6 Solution 1] (Algebra) | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_6#Solution_1 2022 AIME II Problem 6 Solution 1] (Algebra) | ||
| Line 80: | Line 162: | ||
# [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_8#Solution_2_Supplement 2022 AIME II Problem 8 Solution 2 Supplement] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_8#Solution_2_Supplement 2022 AIME II Problem 8 Solution 2 Supplement] (Number Theory) | ||
# [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_8#Solution_3_Supplement 2022 AIME II Problem 8 Solution 3 Supplement] (Number Theory) | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_8#Solution_3_Supplement 2022 AIME II Problem 8 Solution 3 Supplement] (Number Theory) | ||
| − | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_14#Solution_1 2022 AIME II Problem 14 Solution | + | # [https://artofproblemsolving.com/wiki/index.php/2022_AIME_II_Problems/Problem_14#Solution_1 2022 AIME II Problem 14 Solution] (Algebra) |
Latest revision as of 09:12, 19 January 2024
AOPS Contributions
AJHSME
- 1994 AJHSME Problem 25 Solution 2 (Number Theory)
AHSME
- 1991 AHSME Problem 30 Solution 2 (Combinatorics)
- 1994 AHSME Problem 28 Solution 2 (Analytic Geometry)
- 1994 AHSME Problem 29 Solution 2 (Geometry, Trigonometry)
- 1995 AHSME Problem 30 Solution 2 (3D Geometry)
- 1996 AHSME Problem 27 Solution 3 (3D Geometry)
- 1996 AHSME Problem 30 Solution 4 (Geometry, Trigonometry)
- 1996 AHSME Problem 30 Solution 5 (Geometry, Trigonometry)
- 1996 AHSME Problem 30 Solution 6 (Geometry)
- 1997 AHSME Problem 30 Solution 3 (Combinatorics)
- 1998 AHSME Problem 28 Solution 4 (Geometry, Trigonometry)
- 1999 AHSME Problem 25 Solution 4 (Number Theory)
- 1999 AHSME Problem 27 Supplement (Trigonometry)
- 1999 AHSME Problem 28 Solution 2 (Algebra)
- 1999 AHSME Problem 29 Solution 2 (3D Geometry)
AMC 8
- 2004 AMC8 Problem 14 Solution 1 (Geometry)
- 2022 AMC8 Problem 25 Solution 4 (Probability)
- 2022 AMC8 Problem 25 Remark (Probability)
AMC 10
- 2013 AMC10A Problem 24 Graph Theory Insight (Graph Theory)
- 2013 AMC10A Problem 25 Solution 5 (Discrete Geometry)
- 2013 AMC10B Problem 22 Remark (Number Theory)
- 2014 AMC10A Problem 18 Solution 2 (Analytic Geometry)
- 2014 AMC10A Problem 18 Solution 3 (Analytic Geometry)
- 2014 AMC10A Problem 22 Solution 6 (Geometry)
- 2014 AMC10A Problem 22 Solution 7 (Geometry)
- 2015 AMC10A Problem 21 Solution 3 (3D Geometry)
- 2015 AMC10A Problem 22 Solution 4 (Combinatorics)
- 2015 AMC10A Problem 24 Solution 3 (Geometry)
- 2015 AMC10B Problem 19 Solution 3 (Geometry)
- 2016 AMC10A Problem 20 Solution 3 (Combinatorics)
- 2016 AMC10B Problem 19 Solution 4 (Geometry)
- 2016 AMC10B Problem 19 Solution 5 (Geometry)
- 2016 AMC10B Problem 22 Solution 4 (Graph Theory)
- 2016 AMC10B Problem 25 Solution 1 Supplement (Number Theory)
- 2016 AMC10B Problem 25 Solution 3 (Number Theory)
- 2016 AMC10B Problem 25 Solution 4 (Number Theory)
- 2016 AMC10B Problem 25 Remark (Number Theory)
- 2017 AMC10B Problem 17 Solution 4 (Combinatorics)
- 2017 AMC10B Problem 25 Solution 4 (Number Theory)
- 2018 AMC10A Problem 10 Solution 8 (Analytic Geometry)
- 2018 AMC10A Problem 22 Solution 6 (Number Theory)
- 2018 AMC10B Problem 18 Solution 6 (Combinatorics)
- 2018 AMC10B Problem 24 Solution 4 (Geometry)
- 2018 AMC10B Problem 25 Solution 6 (Algebra)
- 2019 AMC10A Problem 22 Solution 3 (Probability)
- 2019 AMC10A Problem 24 Solution 2 (Algebra)
- 2019 AMC10B Problem 22 Solution 4 (Probability, Markov Chain)
- 2019 AMC10B Problem 25 Solution 6 (Combinatorics)
- 2020 AMC10A Problem 20 Solution 7 (Geometry)
- 2020 AMC10A Problem 24 Solution 9 (Number Theory)
- 2020 AMC10A Problem 24 Solution 10 (Number Theory)
- 2020 AMC10A Problem 24 Solution 11 (Number Theory)
- 2020 AMC10B Problem 13 Solution 3 (Combinatorics)
- 2020 AMC10B Problem 21 Solution 6 (Geometry)
- 2020 AMC10B Problem 23 Solution 5 (Group Theory)
- 2020 AMC10B Problem 24 Solution 8 (Algebra)
- 2020 AMC10B Problem 25 Solution 7 (Combinatorics)
- 2021 Spring AMC10A Problem 23 Solution 8 (Probability, Markov Chain)
- 2021 Spring AMC10A Problem 24 Solution 3 (Analytic Geometry)
- 2021 Spring AMC10A Problem 25 Solution 4 (Combinatorics)
- 2021 Spring AMC10B Problem 25 Solution 4 (Analytic Geometry)
- 2021 Spring AMC10B Problem 25 Solution 5 (Analytic Geometry)
- 2021 Spring AMC10B Problem 25 Remark (Analytic Geometry)
- 2021 Fall AMC10A Problem 24 Solution 4 (Graph Theory)
- 2021 Fall AMC10B Problem 12 Solution 1 (Algebra)
- 2021 Fall AMC10B Problem 20 Remark (Probability)
- 2021 Fall AMC10B Problem 23 Solution 2 (Graph Theory)
- 2021 Fall AMC10B Problem 24 Solution 1 (Graph Theory)
AMC 12
- 2000 AMC12 Problem 25 Solution 5 (Graph Theory)
- 2001 AMC12 Problem 22 Solution 5 (Geometry)
- 2001 AMC12 Problem 24 Solution 5 (Geometry, Trigonometry)
- 2002 AMC12A Problem 23 Solution 4 (Geometry)
- 2002 AMC12A Problem 23 Solution 5 (Geometry, Trigonometry)
- 2003 AMC12A Problem 17 Solution 8 (Geometry)
- 2003 AMC12B Problem 21 Solution 2 (Analytic Geometry)
- 2003 AMC12B Problem 25 Solution 3 (Probability)
- 2007 AMC12B Problem 23 Solution 3 (Geometry)
- 2009 AMC12B Problem 24 Solution 4 (Trigonometry)
- 2010 AMC12A Problem 23 Remark (Number Theory)
- 2010 AMC12B Problem 23 Solution 4 (Algebra)
- 2011 AMC12B Problem 20 Solution 6 (Geometry, Trigonometry)
- 2012 AMC12B Problem 17 Solution 6 (Geometry, Trigonometry)
- 2012 AMC12B Problem 18 Solution 5 (Combinatorics)
- 2012 AMC12B Problem 19 Solution 3 (3D Geometry)
- 2012 AMC12B Problem 20 Solution 2 (Geometry)
- 2012 AMC12B Problem 21 Solution 4 (Geometry, Trigonometry)
- 2013 AMC12A Problem 16 Solution 4 (Algebra)
- 2013 AMC12A Problem 18 Solution 3 (3D Geometry)
- 2013 AMC12B Problem 24 Solution 6 (Geometry)
- 2013 AMC12B Problem 25 Solution 3 (Algebra)
- 2014 AMC12A Problem 20 Remark (Geometry)
- 2014 AMC12A Problem 22 Solution 2 (Number Theory)
- 2014 AMC12B Problem 21 Solution 6 (Geometry)
- 2014 AMC12B Problem 22 Remark (Probability, Markov Chain)
- 2014 AMC12B Problem 24 Solution 4 (Geometry)
- 2016 AMC12A Problem 20 Solution 5 (Algebra)
- 2016 AMC12A Problem 21 Remark (Geometry)
- 2016 AMC12B Problem 15 Solution 4 (Combinatorics)
- 2017 AMC12A Problem 22 Remark (Probability, Markov Chain)
- 2017 AMC12A Problem 24 Solution 4 (Geometry, Trigonometry)
- 2017 AMC12A Problem 25 Solution 6 (Algebra & Probability)
- 2017 AMC12B Problem 22 Solution 5 (Probability)
- 2017 AMC12B Problem 24 Solution 3 (Geometry)
- 2018 AMC12A Problem 21 Solution 4 (Algebra)
- 2018 AMC12A Problem 21 Solution 5 (Algebra)
- 2018 AMC12A Problem 21 Solution 6 (Algebra)
- 2018 AMC12B Problem 25 Solution 6 (Geometry, Trigonometry)
- 2019 AMC12A Problem 20 Solution 4 (Probability)
- 2020 AMC12A Problem 24 Solution 9 (Geometry, Trigonometry)
- 2020 AMC12B Problem 25 Solution 2 (Trigonometry)
- 2020 AMC12B Problem 25 Solution 4 (Calculus)
- 2021 Spring AMC12A Problem 24 Solution 5 (Geometry, Trigonometry)
- 2021 Spring AMC12B Problem 18 Solution 2 (Algebra)
- 2021 Spring AMC12B Problem 20 Solution 7 (Algebra)
- 2021 Spring AMC12B Problem 24 Solution 6 (Geometry)
- 2021 Fall AMC12B Problem 24 Solution 1 (Geometry, Trigonometry)
- 2022 AMC12A Problem 20 Solution 5 (Geometry, Trigonometry)
- 2022 AMC12A Problem 23 Solution 5 (Calculus)
- 2022 AMC12A Problem 25 Solution 3 (Geometry, Number Theory)
- 2022 AMC12B Problem 19 Solution 3 (Geometry, Trigonometry)
- 2022 AMC12B Problem 24 Supplement (Trigonometry)
- 2022 AMC12B Problem 25 Solution 3 (Geometry)
- 2023 AMC12A Problem 20 Solution 3 (Combinatorics)
- 2023 AMC12A Problem 21 Solution 6 (Probability)
- 2023 AMC12A Problem 25 Solution 1 (Trigonometry)
- 2023 AMC12B Problem 16 Solution 3 (Number Theory)
- 2023 AMC12B Problem 17 Solution 2 (Geometry, Trigonometry)
- 2023 AMC12B Problem 17 Solution 3 (Geometry, Trigonometry)
- 2023 AMC12B Problem 18 Solution 3 (Algebra)
- 2023 AMC12B Problem 20 Solution 1 (Geometry, Trigonometry)
- 2023 AMC12B Problem 25 Supplement (Geometry, Trigonometry)
AIME
- 1983 AIME Problem 4 Solution 6 (Geometry, Trigonometry)
- 1983 AIME Problem 7 Solution 7 (Combinatorics)
- 1985 AIME Problem 12 Solution 5 (Probability)
- 1997 AIME Problem 9 Solution 4 (Algebra)
- 2001 AIME II Problem 9 Solution 3 (Combinatorics)
- 2021 AIME I Problem 12 Solution 2 (Probability, Markov Chain)
- 2021 AIME I Problem 12 Remark (Probability, Markov Chain)
- 2021 AIME II Problem 8 Solution 2 (Probability, Markov Chain)
- 2021 AIME II Problem 8 Remark (Probability, Markov Chain)
- 2022 AIME I Problem 8 Solution 2 (Geometry)
- 2022 AIME II Problem 2 Solution (Probability)
- 2022 AIME II Problem 5 Solution 1 (Number Theory)
- 2022 AIME II Problem 6 Solution 1 (Algebra)
- 2022 AIME II Problem 7 Solution 1 (Geometry)
- 2022 AIME II Problem 8 Solution 2 Supplement (Number Theory)
- 2022 AIME II Problem 8 Solution 3 Supplement (Number Theory)
- 2022 AIME II Problem 14 Solution (Algebra)
