18. Distribution of Money. Nine friends $A, B, C, D, E, F, G$, $H, K$, gathering one evening to spend time together, did the following. First, $A$ gave each of the other eight people as much money as they already had. Then $B, C$, and so on up to $K$ did the same. After this, it turned out that all nine friends had the same amount of money.

Can you find the smallest sum in cents that each of the participants could have had initially?
18. The smallest sum (in cents) that one of the participants could have must exceed the number of participants by one. The sums belonging to the other participants can be found by sequential doubling and subtracting 1. Thus, we get \(10,19,37,73,145,289,577,1153\) and 2305 cents. Let the one with the most money start first. Then, in the end, each participant will have \(2^{9}\) (512) cents, that is, 5 dollars and 12 cents.