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A group of at least 5 jealous professors are locked in a room. There is nothing else in the room but pencils and one tiny scrap of paper per person. The professors want to determine their average (mean, not median) salary so that each one can gloat or grieve over their 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 "3 people earn more than $\$$40,000" or "no one earns more than $\$$90,000" are not allowed.

Please note: I just made the minimum of the group size $5$ arbritrarily, in order to avoid trivial cases.

Source: The Art and Craft of Problem Solving by Paul Zeitz

Sorry I did not know what to tag this.

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