MathDB

Given a table in a form of the regular

1000

-gon with sidelength

1

. A Beetle initially is in one of its vertices. All

1000

vertices are numbered in some order by numbers

1

2

\ldots

1000

so that initially the Beetle is in the vertex

1

. The Beetle can move only along the edges of

1000

-gon and only clockwise. He starts to move from vertex

1

and he is moving without stops until he reaches vertex

2

where he has a stop. Then he continues his journey clockwise from vertex

2

until he reaches the vertex

3

where he has a stop, and so on. The Beetle finishes his journey at vertex

1000

. Find the number of ways to enumerate all vertices so that the total length of the Beetle's journey is equal to

2017

Problem Statement