( "Sisyphian Labour" )
There are 1001 steps going up a hill , with rocks on some of them {no more than 1 rock on each step ) . Sisyphus may pick up any rock and raise it one or more steps up to the nearest empty step . Then his opponent Aid rolls a rock (with an empty step directly below it) down one step . There are 500 rocks, originally located on the first 500 steps. Sisyphus and Aid move rocks in turn , Sisyphus making the first move . His goal is to place a rock on the top step.
Can Aid stop him?( S . Yeliseyev) combinatoricsgamegame strategy