MathDB

Let

n\geq 2

be an integer.

3n

distinct points are plotted on the circle, where A and B perform the following operation : Firstly,

A

picks exactly 2 points which haven't been connected yet and connects them by a segment. Secondly, B picks exactly 1 point with no piece and place a piece. Prove that, after consecutive

n

operations, despite how B acts, A can make the number of segments no less than

\displaystyle \frac{n-1}{6}

, which connect a point with a piece and a point with no piece.

4

Problems(1)