You should be able to solve this.

A group of jealous professors is locked up in
a room. There is nothing else in the room but pencils
and one tiny scrap of paper per person. The profes-
sors want to determine their average (mean, not me-
dian) salary so that each one can gloat or grieve over
his or her personal situation compared to their peers.
However, they are secretive people, and do not want to
give away any personal salary information to anyone
else. Can they determine the average salary in such a
way that no professor can discover any fact about the
salary of anyone but herself? For example, even facts
such as "three people earn more than $40,000" or "no
one earns more than $90,000" are not allowed.

>>10. I assume you are refining the method in >>9. For the nth guy, the n-1th guy and the n+1th guy can work together to figure out his salary. The n-1th guy and n+1th guy have enough information from the first go-round to determine (nth guys salary + random number) and enough information from the second go-round to determine (random number), which combined give you the nth guy's salary.