Difference between revisions of "2019 AIME II Problems/Problem 5"
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+ | ==Problem== | ||
+ | Four ambassadors and one advisor for each of them are to be seated at a round table with <math>12</math> chairs numbered in order <math>1</math> to <math>12</math>. Each ambassador must sit in an even-numbered chair. Each advisor must sit in a chair adjacent to his or her ambassador. There are <math>N</math> ways for the <math>8</math> people to be seated at the table under these conditions. Find the remainder when <math>N</math> is divided by <math>1000</math>. | ||
+ | ==Solution== | ||
+ | ==See Also== | ||
+ | {{AIME box|year=2019|n=II|num-b=4|num-a=6}} | ||
+ | {{MAA Notice}} |
Revision as of 17:58, 22 March 2019
Problem
Four ambassadors and one advisor for each of them are to be seated at a round table with chairs numbered in order to . Each ambassador must sit in an even-numbered chair. Each advisor must sit in a chair adjacent to his or her ambassador. There are ways for the people to be seated at the table under these conditions. Find the remainder when is divided by .
Solution
See Also
2019 AIME II (Problems • Answer Key • Resources) | ||
Preceded by Problem 4 |
Followed by Problem 6 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.