MathDB

Let

N\geq 4

be a fixed positive integer. Two players,

A

and

B

are forming an ordered set

\{x_1,x_2,...\},

adding elements alternatively.

A

chooses

x_1

to be

1

-1,

then

B

chooses

x_2

to be

2

-2,

then

A

chooses

x_3

to be

3

-3,

and so on. (at the

k^{th}

step, the chosen number must always be

k

-k

)
The winner is the first player to make the sequence sum up to a multiple of

N.

Depending on

N,

find out, with proof, which player has a winning strategy.

Problem Statement