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Timothy Chow
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There are $n$ men, standing one at each vertex of a convex $n$-gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are there to do so without meeting another one?

See OEIS A350599 for the first few numerical values.

There are $n$ men, standing one at each vertex of a convex $n$-gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are there to do so without meeting another one?

There are $n$ men, standing one at each vertex of a convex $n$-gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are there to do so without meeting another one?

See OEIS A350599 for the first few numerical values.

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YCor
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There are n number of$n$ men, standing one at each vertex of a convex n $n$- gongon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, howhow many different ways are there to do so without meeting another one?

There are n number of men standing one at each vertex of a convex n - gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are there to do so without meeting another one?

There are $n$ men, standing one at each vertex of a convex $n$-gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are there to do so without meeting another one?

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Combinatorics related plane geometry

There are n number of men standing one at each vertex of a convex n - gon. If they are allowed to move together along sides or diagonals of the polygon to reach another vertex, how many different ways are there to do so without meeting another one?