Consider the following game. The rules are as follows: There is an unlimited supply of identical coins, each with radius s > 0. Each player takes turns to place coins inside a shaded region. The coins cannot overlap, and they must lie entirely inside the shaded region. The first player who cannot put down a coin will lose the game. Consider the shaded region B, which is an annulus bounded by two circles with radius r(> s) and R(> 3r) respectively. Is it true that one of two players has a winning strategy ?
I know that there is not a winning strategy, but how to prove it?