Divisor Game

Problem

Given n, two players alternate choosing a divisor x of n with 0 < x < n and subtract it from n; the player who cannot move loses. Return True if the first player wins.

The first player wins exactly when n is even and greater than 1, because choosing 1 forces an odd number onto the opponent. For n = 1 there is no move and the first player loses.

Hint

Every odd n can only be reduced to an even number by the only odd divisor, 1.

Test cases

case 1

in: [2]

expected: true

case 2

in: [3]

expected: false

case 3

in: [4]

expected: true

case 4

in: [1]

expected: false

case 5

in: [9]

expected: false

case 6

in: [10]

expected: true

Starter codePython

def divisor_game(n):
    # Your code here
    pass

6 test cases · run your code against them in the editor