[beefnugs]

Why is this a great riddle? It sounds like incomplete nonsense to me:

It doesnt say anything about the skill levels of the participants, whether their answers are just guessing, or why they arent just guessing the sum of the other two people each time asked to provide more information?

It doesnt say the guy saying 65 is even correct

How could three statements of "no new information" give information to the first guy that didn't know the first time he was asked?

[DangitBobby]

2 and 3 saying they don't know eliminates some uncertainties 1 had about their own number (any combination where the other two would see numbers that could tell them their own). After those possibilities were eliminated, the 1st person has narrowed it down enough to actually know based on the numbers shown above the other 2. The puzzle could instead have been done in order 2, 3, 1 and 1 would not have needed to go twice.

I guess really the only missing information is that they have the exact same information you do, plus the numbers above their friends heads.

[Nition]

> The puzzle could instead have been done in order 2, 3, 1 and 1 would not have needed to go twice.

If this is true, then back in the original 1->2->3->1 form, shouldn't person #3 have been able to answer it?