MathDB

Arne and Berit are playing a game. They have chosen positive integers

m

and

n

with

n\geq 4

and

m \leq 2n + 1

. Arne begins by choosing a number from the set

\{1, 2, \dots , n \}

, and writes it on a blackboard. Then Berit picks another number from the same set, and writes it on the board. They continue alternating turns, always choosing numbers that are not already on the blackboard. When the sum of all the numbers on the board exceeds or equals

m

, the game is over, and whoever wrote the last number has won. For which combinations of

m

and

n

does Arne have a winning strategy?

Problem Statement