The correct answer is: Only I and II follow.
The first statement is “Some boxes are hammers.” This means that there is at least one box that is also a hammer. The second statement is “Some hammers are beads.” This means that there is at least one hammer that is also a bead. The third statement is “All beads are rings.” This means that all beads are rings.
The first conclusion is “Some rings are hammers.” This conclusion is not valid because the first statement only says that some boxes are hammers, not that all boxes are hammers. It is possible that there are boxes that are not hammers, and therefore it is possible that there are rings that are not hammers.
The second conclusion is “Some hammers are boxes.” This conclusion is valid because the first statement says that some boxes are hammers, and the third statement says that all beads are rings. Therefore, some hammers must be boxes, because some boxes are beads.
The third conclusion is “Some rings are boxes.” This conclusion is not valid because the first statement only says that some boxes are hammers, not that all boxes are hammers. It is possible that there are boxes that are not hammers, and therefore it is possible that there are rings that are not boxes.
Therefore, the only valid conclusions are I and II.