2023 AIME I Problems
2023 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
Instructions
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Contents
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
Problem 2
Positive real numbers and satisfy the equations The value of is where and are relatively prime positive integers. Find
Problem 3
A plane contains 40 lines, no 2 of which are parallel. Suppose that there are 3 points where exactly 3 lines intersect, 4 points where exactly 4 lines intersect, 5 points where exactly 5 lines intersect, 6 points where exactly 6 lines intersect, and no points where more than 6 lines intersect. Find the number of points where exactly 2 lines intersect.
Problem 4
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
Problem 5
Let be a point on the circle circumscribing square that satisfies and . Find the area of .
Problem 6
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
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.
Problem 8
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
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.
Problem 10
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
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.
Problem 12
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
Problem 13
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
Problem 14
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
Problem 15
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
See also
2023 AIME I (Problems • Answer Key • Resources) | ||
Preceded by 2022 AIME II |
Followed by 2023 AIME II | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
- 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.