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 10-5-3-2-1.
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 2014-02-25 14:09:52