Y by Adventure10
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 one unit 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?





![$[0, n]$](http://latex.artofproblemsolving.com/a/5/8/a585433224883cbcd304f34129a152b97d5ed96e.png)


![$[0, n]$](http://latex.artofproblemsolving.com/a/5/8/a585433224883cbcd304f34129a152b97d5ed96e.png)





This post has been edited 2 times. Last edited by Welp..., Feb 6, 2020, 6:14 PM
Reason: better title than generic
Reason: better title than generic