MathDB

Let

n \ge 3

be an integer. Zagi the squirrel sits at a vertex of a regular

n

-gon. Zagi plans to make a journey of

n-1

jumps such that in the

i

-th jump, it jumps by

i

edges clockwise, for

i \in \{1, \ldots,n-1 \}

. Prove that if after

\lceil \tfrac{n}{2} \rceil

jumps Zagi has visited

\lceil \tfrac{n}{2} \rceil+1

distinct vertices, then after

n-1

jumps Zagi will have visited all of the vertices. (Remark. For a real number

x

, we denote by

\lceil x \rceil

the smallest integer larger or equal to

x

Problem Statement