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
I thought Sam did put on the ring in the books.
It also affected Boromir just being around it.
Didn't Smeagol kill a friend just to have it before even wearing it?
Yes. Basically, Sam was practically only one in the Fellowship who could resist the temptations of The Ring, because he had really simple desires.
Sam Bombadil