2023 AIME I Problems

2023 AIME I (Answer Key) | AoPS Contest Collections • PDF

Instructions This is a 15-question, 3-hour examination. All answers are integers ranging from to , inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers. No aids other than scratch paper, graph paper, ruler, compass, and protractor are permitted. In particular, calculators and computers are not permitted.

1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

Note: the times listed are in GMT

Problem 1

Five men and nine women stand equally spaced around a circle in random order. The probability that every man stands diametrically opposite a woman is where and are relatively prime positive integers. Find

Solution

Problem 2

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 3

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 4

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 5

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM. Unofficial problem statement has been posted.

Solution

Problem 6

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 7

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM. Unofficial problem statement has been posted.

Solution

Problem 8

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 9

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM. Unofficial problem statement has been posted.

Solution

Problem 10

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 11

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM. Unofficial problem statement has been posted.

Solution

Problem 12

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 13

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 14

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

Problem 15

These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.

Solution

See also

• American Invitational Mathematics Examination
• AIME Problems and Solutions
• Mathematics competition resources

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.