Other physics-based solutions
fresco wrote:
This situation is in some ways similar to the weight of a plane carrying a flying bird. The total weight is the plane plus all its contents irrespective of their positions.
True, if the system is static--if the position of the bird is accelerating downward, then the plane _does_ weigh less (stand on a scale and sudden drop and see what your weight does); however, the bird can only fall a short way, so averaged over any reasonable time period, the plane's weight is constant.
Therefore, if the archeologist were to begin crossing the bridge with the artifacts held high above his head and allow them to fall (accelerate downward) as he crossed, the bridge would not have to support the entire weight. But that would require him to cross extremely quickly.
Or, he could tie a rope around one and let it fall off the bridge as he crossed. That would give him more time to get across the bridge. Once on the other side, he could then pull the artifact up.