If we assume our juggler is not Superman and must cross the bridge juggling
, then if he intends to keep the pins in the air for 4 seconds, then for every pin he accelerates into the air, its inertia causes the pin to experience 5 g's, as Kal said. So each pin weighs as much as five pins when accelerating. So after you apply Newton's third law, the juggler's weight, plus the accelerating pin's weight equals 57kg. This seems like the kind of logic the answer would work on.
Although, I assume the 'weight' of the pins would change depending on how high they were thrown. If the pins only had to stay in the air for 1 second (he must be a VERY skilled juggler
), would that make it possible for the juggler to cross the bridge?