We observe that whoever scored the bullseye must also have scored a 3, since the only way to make 21 out of the remaining five shots, given the constraints in the problem, would be 105321.
Riley obviously didn't score the bullseye.
Suppose Reuben scored a 3. Then by symmetry, we'd have no way of determining whether Ricardo or Reuben scored the bullseye (and thus the puzzle wouldn't have unique a solution).
So we must assume that Reuben did not score a 3, and thus Ricardo scored the bullseye.

Posted by tomarken
on 20140225 14:09:52 