Find the initial amount
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Nine persons in a party, A, B, C, D, E, F, G, H, K, did as follows: First A gave each of the others as much money as he (the receiver) already held; then B did the same; then C; and so on to the last, K giving to each of the other eight persons the amount the receiver then held. Then it was found that each of the nine persons held the same amount. Can you find the smallest amount in cents that each person could
have originally held?
The smallest number originally held by one person will be (in cents) one more than the number of persons. The others can be obtained by continually
doubling and deducting one. So we get their holdings as 10, 19,37, 73, 145, 289,577, 1,153, and 2,305. Let the largest holder start the payment and work backwards, when the number of cents in the end held by each person will be 29 or 512-that is, $5.12.
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