This curious game was invented by Princeton mathematician John H. Conway.
Two players take turns naming positive integers, but an integer is off limits if it's the sum of nonnegative multiples of integers already been named.
Once 1 is named, everything is off limits (because no new positive integer can be named).
A player forced to name "1" - i.e. having no other choice loses the game.
Devise a winning strategy for the 1st player.