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
Ah yes, tape, the cornerstone of every Hobbit's hole.
Did you read the title?
invents tape, then tapes your mouth shut