Recently I was talking to a friend as he was recovering a nine foot Diamond table and he was telling me about a bet he was offered. A guy wanted to bet him that he could break a rack of 9 ball on a table without rails installed and all balls would be knocked off the table. My friend accepted the bet and the challenger thought about it and cancelled the bet. Obviously, after the break all balls must move enough to contact a rail if it they were to be able to fall off and I can't remember ever seeing that happen. With enough cue ball speed I think it could be done but how much speed must be generated? I figure there are enough mathematicians on the forum to provide the answer.