866
But first they would need to invent some tape
(i.imgur.com)
They could have fitted the whole ring / tape / mouse assembly into a small paper bag Aragorn could have kept it in his jacket and fed it little bits of lembas on the way how lovely x
He really was, though. Both Frodo and Bilbo carried the weight better than any other had before them, but they were still negatively impacted by it. But not Sam. Truly a goldenhearted being.