Bela and Jenn play the following game on the closed interval of the real number line, where is a fixed integer greater than . They take turns playing, with Bela going first. At his first turn, Bela chooses any real number in the interval . Thereafter, the player whose turn it is chooses a real number that is more than two units away from all numbers previously chosen by either player. A player unable to choose such a number loses. Using optimal strategy, which player will win the game?
Bela will always win.
Jenn will always win.
Bela will win if and only if is odd.
Jenn will win if and only if is odd.
Jenn will win if and only if .
