Ten people sit at a round table. The sum of Rupees 10 is to be distributed among them so that each person receives the average of what each of his two neighbours receives.

In how many different ways can this be achieved ?
[Given: 1 Rupee = 100 Paise]

(In reply to solution by Charlie)

Charlie wrote: ----
If more than one, then at least two must be adjacent to at least one neighbor with less, and again would have more than the average of his two neighbors.
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Sorta. The situation where everyone gets 1 rupee has more than one person having the max (namely, everyone).

A better way to prove is by contradiction. Suppose there was a solution where not everyone had the same amount. Then, there are (at least) two neighbors A and B where A > B. Since B = 1/2*(A+C), C is the next person over, we have B > C. Iterating, we have A > B > C > ... J > A, a contradiction.

Posted by jakl on 2003-05-30 03:45:52