I'm going with the one on gravel, unless the pusher has microspikes while on ice.
Discussion
When one is taking the question literaly, it would be eighter one of the two ice. Nowhere in the question there is a requirement for the object to move. It is questioned for the least force. So one could say, when the person slides on the ice, the force on the object should be smaller then the force on the round object on gravel.
Ha, I never even considered that the object didnt need to move. Makes sense
