MathDB

Let

n \geq 2

and

m

be positive integers.

m

ballot boxes are placed in a line. Two players

A

and

B

play by turns, beginning with

A

, in the following manner. Each turn,

A

chooses two boxes and places a ballot in each of them. Afterwards,

B

chooses one of the boxes, and removes every ballot from it.

A

wins if after some turn of

B

, there exists a box containing

n

ballots. For each

n

, find the minimum value of

m

such that

A

can guarantee a win independently of how

B

plays.

Problem Statement