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]

Only 1 way: each person gets 1 rupee.

If there were different amounts, some one or more than one would have to have the largest amount. If only 1 then this person would have more than the average of his two neighbors. 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.

Posted by Charlie on 2003-05-30 03:08:31