Difference between revisions of "2019 AIME II Problems/Problem 5"

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==Problem==
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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>.
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==Solution==
  
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==See Also==
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{{AIME box|year=2019|n=II|num-b=4|num-a=6}}
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{{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 $12$ chairs numbered in order $1$ to $12$. Each ambassador must sit in an even-numbered chair. Each advisor must sit in a chair adjacent to his or her ambassador. There are $N$ ways for the $8$ people to be seated at the table under these conditions. Find the remainder when $N$ is divided by $1000$.

Solution

See Also

2019 AIME II (ProblemsAnswer KeyResources)
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

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