Problem of the Month(s)

The POM Author (artist's rendering)

The POM Author (artist’s rendering)

In the hustle-bustle of finals, you may have missed that the Grand Vizier of monthly problems posted the December Problem of the Month.  You can read it here.

Don’t be alarmed by the fact that December is more than half over, though, because this is also the Problem of the Month for January.  So you have until the end of next month to get your solutions in.

Here’s the problem:

Four (shy) mathematicians are sitting around a table and want to know the average of their salaries. The problem is, none of them wants to reveal their salary to anyone else at the table. Is it possible to develop a scheme by which they can compute this average without spilling the beans on their salary?

Problem 1: Develop a scheme that our mathematicians can use to compute the average salary, without any one person knowing the salary of anyone else.

What if one of these four does not mind divulging his salary so that he is able determine the other three salaries, is it possible to construct a scheme to compute the average without revealing all the salaries?

Problem 2: Develop a scheme that the above mathematicians can use to compute the average of their salaries, without divulging the salary of anyone who wants to keep it secret.

— from the POM webpage

Just the thing to stimulate your mind while pretending to listen to your uncle drone on and on about who knows what during the family dinner!