MathDB

Anna and Orjan play the following game: they start with a positive integer

n>1

, Anna writes it as the sum of two other positive integers,

n = n_1+n_2

. Orjan deletes one of them,

n_1

n_2

. If the remaining number is larger than

1

, the process is repeated, i.e. Anna writes it as the sum of two positive integers,

n_3+n_4

, Orjan deletes one of them etc. The game ends when the last number is

1

. Orjan is the winner if there are two equal numbers among the numbers he has deleted, otherwise Anna wins. Who is winning the game if n = 2008 and they both play optimally?

Problem Statement