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]
Hmmm.. that got cut off for some reason. Let's try again.
If not all the sums are equal, then let's assume A<C. B sitting in between gets the average amount, which will be something in the middle, i.e., A<B<C. And since C is the average of B and D, and B<C, we can conclude B<C<D. And so on around the table, until we get to I<J<A. Which means A<B...<J<A, or A<A. Which contradicts our initial assumption, reductio ad absurdum.
So we must conclude all the sums were equal, and each got 1 rupee.
first try (again...)
