490. Five bandits took a wallet filled with ducats from a passerby. The strongest of them took 81 ducats, and each of the other four took a different amount. Due to the unequal division, a dispute arose, and the ataman who arrived at that time ordered the one who took the most to double the number of ducats each of the others had, and then the one who took the second largest amount to do the same, followed by the one who took the third, fourth, and fifth largest amounts. As a result, each of the five bandits ended up with the same number of ducats. Determine how many ducats were in the wallet and how many each took initially.

## Problems from "Traitè de Géometrie" by E. Rouché et Ch. de-Comberousse.
490. Instruction. At the end of the section, each has $\frac{1}{5}$ of the total, so before doubling, four have $\frac{1}{10}$ each, and the fifth has $\frac{6}{10}$; before the second doubling, the first three have $\frac{1}{20}$ each, the fourth has $\frac{11}{20}$, and the fifth has $\frac{6}{20}$; before the third doubling, the first two have $\frac{1}{40}$ each, the third has $\frac{21}{40}$, the fourth has $\frac{11}{40}$, and the fifth has $\frac{6}{40}$; before the fourth doubling, the first has $\frac{1}{80}$, the second has $\frac{41}{80}$, the third has $\frac{21}{80}$, the fourth has $\frac{11}{80}$, and the fifth has $\frac{6}{80}$; before the fifth doubling, the first has $\frac{81}{160}$, the second has $\frac{41}{160}$, the third has $\frac{21}{160}$, the fourth has $\frac{11}{16 \text { i) }}$, and the fifth has $\frac{6}{160}$. But since the first has 81 ducats, the total was 160 ducats.

Rouché, E. and Comberousse, Ch. - French mathematicians who collaborated on the preparation of courses and textbooks, which enjoy well-deserved fame.