Question 77
Let $S$ be a finite set with $n \ge 2$ elements. Two players, $A$ and $B$, alternately choose nonempty proper subsets of $S$, where
(1) it is not allowed to choose a set that contains a set previously chosen by any player,
(2) it is not allowed to choose a set that is contained in any previously chosen set,
(3) it is not allowed to choose a set whose union with any previously chosen set is $S$.
$A$ begins. The player who first cannot choose a set anymore loses. Which player has a winning strategy?
(1) it is not allowed to choose a set that contains a set previously chosen by any player,
(2) it is not allowed to choose a set that is contained in any previously chosen set,
(3) it is not allowed to choose a set whose union with any previously chosen set is $S$.
$A$ begins. The player who first cannot choose a set anymore loses. Which player has a winning strategy?