Problem 5. Alice and Bazza are playing the inekoalaty game, a two-player game whose rules depend on a positive real number λ which is known to both players. On the n^th turn of the game (starting with n = 1) the following happens:

• If n is odd, Alice chooses a nonnegative real number x_n such that

x₁+x₂+ ...+x_n≤λn

• If n is even, Bazza chooses a nonnegative real number x_n such that

$$x_1^2+x_2^2+\mathrm{...}+x_n^2\le n$$

If a player cannot choose a suitable number x_n, the game ends and the other player wins. If the game goes on forever, neither player wins. All chosen numbers are known to both players.

Determine all values of λ for which Alice has a winning strategy and all those for which Bazza has a winning strategy.