Question 4
On an infinite regular hexagonal grid, initially empty, players $A,B$ alternate, with $A$ first. On her turn $A$ puts counters in two adjacent empty cells; on his turn $B$ removes any one counter. $A$ wins as soon as $k$ consecutive cells in one line are occupied. Find the least positive $k$ for which $A$ cannot force a win in finitely many moves, or show no such minimum exists.
Proposed by Palmer Mebane (as credited in the supplied compilation).
Proposed by Palmer Mebane (as credited in the supplied compilation).