Y by
Let
be a finite abelian group. There is a magic box
. At any point, an element of
may be added to the box and all elements belonging to the subgroup (of
) generated by the elements currently inside
are moved from outside
to inside (unless they are already inside). Initially
contains only the group identity,
. Alice and Bob take turns moving an element from outside
to inside it. Alice moves first. Whoever cannot make a move loses. Find all
for which Bob has a winning strategy.









