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2020 AIME II Problems

2020 AIME II (Answer Key)
Printable version | AoPS Contest Collections • PDF

Instructions

  1. This is a 15-question, 3-hour examination. All answers are integers ranging from $000$ to $999$, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.
  2. No aids other than scratch paper, rulers and compasses are permitted. In particular, graph paper, protractors, calculators and computers are not permitted.
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

Problem 1

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 2

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 3

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Solution

Problem 4

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 5

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 6

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 7

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 8

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 9

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 10

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Solution

Problem 11

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Solution

Problem 12

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 13

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 14

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

Problem 15

Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks! Scorpio Sucks!

Solution

2020 AIME II (Problems • Answer Key • Resources)
Preceded by
2020 AIME I Problems 		Followed by
2021 AIME I Problems
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
All AIME Problems and Solutions

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