MathDB

Consider the real number axis (i. e. the

x

-axis of a Cartesian coordinate system). We mark the points

1

2

, ...,

2n

on this axis. A flea starts at the point

1

. Now it jumps along the real number axis; it can jump only from a marked point to another marked point, and it doesn't visit any point twice. After the (

2n-1

)-th jump, it arrives at a point from where it cannot jump any more after this rule, since all other points are already visited. Hence, with its

2n

-th jump, the flea breaks this rule and gets back to the point

1

. Assume that the sum of the (non-directed) lengths of the first

2n-1

jumps of the flea was

n\left(2n-1\right)

. Show that the length of the last (

2n

-th) jump is

n

Problem Statement