## Task $7 / 63$

Ten buckets of the same size and appearance are filled with coins that look identical. In nine of these buckets, each coin weighs 10 g, while in one bucket they weigh 11 g.

How can one determine with a single weighing which bucket contains the coins weighing 11 g?
Place the buckets in a row and take one coin from the first, two coins from the second, three coins from the third, and so on until you take ten coins from the tenth. In this way, you will have finally taken 55 coins, which you weigh in total to the nearest whole gram.

If the coins with a mass of $11 \mathrm{~g}$ were in the $n$-th bucket, then among these 55 coins, $n$ pieces have a mass of $11 \mathrm{~g}$ and $(55-n)$ pieces have a mass of $10 \mathrm{~g}$. The total mass $G$ is therefore (in grams)

$$
G=(55-k) \cdot 10+11 \cdot n=550+n
$$

Then, however, $n=G-550 . n$ is the number of the bucket in which the sought-after coins are located.