Ondra spent $\frac{2}{3}$ of his money on a trip and then gave $\frac{2}{3}$ of the remainder to a school for children from Tibet. He then spent $\frac{2}{3}$ of the new remainder on a small gift for his mother. From the remaining money, he lost $\frac{4}{5}$ due to a hole in his pocket, and when he gave half of what was left to his little sister, he was left with exactly one crown. With what amount $S$ did Ondra go on the trip?

(M. Volfová)
The number of Ondra's crowns before the trip is denoted as $x$.

- Ondra spent $\frac{2}{3}$ of his money on the trip, leaving him with $\frac{1}{3} x$ crowns.
- He donated $\frac{2}{3}$ of the remaining money to a school in Tibet, leaving him with $\frac{1}{3} \cdot \frac{1}{3} x=\frac{1}{9} x$ crowns.
- The gift for his mother cost $\frac{2}{3}$ of the remainder, leaving him with $\frac{1}{3} \cdot \frac{1}{9} x=\frac{1}{27} x$ crowns.
- He lost $\frac{4}{5}$ of what was left, leaving him with $\frac{1}{5} \cdot \frac{1}{27} x=\frac{1}{135} x$ crowns.
- He gave half of the remaining money to his sister, leaving him with the other half, $\mathrm{i.e.} \cdot \frac{1}{2} \cdot \frac{1}{135} x=\frac{1}{270} x$, which was 1 crown.

If $\frac{1}{270} x=1$, then $x=270$. Ondra went on the trip with an amount of 270 crowns.

Another solution. The problem can also be solved by working backwards according to the following scheme:

![](https://cdn.mathpix.com/cropped/2024_04_17_faa98acd9497c1119dfag-2.jpg?height=137&width=1391&top_left_y=1419&top_left_x=367)

Step by step, from right to left, we get the following values: $1 \cdot 2=2, 2 \cdot 5=10, 10 \cdot 3=30$, $30 \cdot 3=90$ and $90 \cdot 3=270$. Ondra had 270 crowns before the trip.