Question 44
Let $n \ge 2$ be an integer. There are $n$ distinct circles on the plane such that any two circles have two distinct intersections and no three circles have a common intersection. Initially there is a coin on each of the intersection points of the circles. Starting from $X$, players $X$ and $Y$ alternately take away a coin, with the restriction that one cannot take away a coin lying on the same circle as the last coin just taken away by the opponent in the previous step. The one who cannot do so will lose. In particular, one loses when there is no coin left. For what values of $n$ does $Y$ have a winning strategy?