Difference between revisions of "2023 AIME I Problems"
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Note: the times listed are in GMT | Note: the times listed are in GMT | ||
==Problem 1== | ==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 <math>\frac{m}{n},</math> where <math>m</math> and <math>n</math> are relatively prime positive integers. Find <math>m+n.</math> | |
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[[2023 AIME I Problems/Problem 1|Solution]] | [[2023 AIME I Problems/Problem 1|Solution]] | ||
Revision as of 12:52, 8 February 2023
| 2023 AIME I (Answer Key) | AoPS Contest Collections • PDF | ||
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Instructions
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| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
to 
, inclusive. Your score will be the number of correct answers; i.e., there is neither partial credit nor a penalty for wrong answers.Note: the times listed are in GMT
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
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
Problem 3
These problems will not be available until the 2023 AIME I is released on February 8th, 2023, at 12:00 AM.
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
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 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. 
