[aardvarkr]

I think it has something to do with applying the lower bound of 1.

If p1 KNOWS that he’s the largest then he has to have gained some other piece of information. Say the numbers he sees are 32 and 33. His number would have to be either 1 or 65. If p1 was 1 then the other two would have known p1 couldn’t be the sum of the other two

[oezi]

But p2 and p3 don't yet know what they are themselves just because they see a 1:

If p2 sees 1 and 33, s/he would wonder if s/he is 32 or 34.

P3 would consider 31 or 33.