2. The pond has a square shape. On the first frosty day, the part of the pond within 10 meters of the nearest shore froze. On the second day, the part within 20 meters froze, on the third day, the part within 30 meters, and so on. On the first day, the area of open water decreased by $19 \%$. How long will it take for the pond to freeze completely?
Solution. It is not hard to understand that a pond of $200 \times 200$ fits, for which the answer is - in 10 days (since each day the side decreases by 20 meters). There are no other options, as the larger the side of the pond, the smaller the percentage that will freeze on the first day.

More rigorously: let the side of the pond be $x$ meters, then the initial area is $x^{2}$ m $^{2}$; then after the first day, $0.81 x^{2}=(0.9 x)^{2}$ remains, that is, the side of the pond after the first day is $0.9 x$. Therefore, the side decreased by $0.1 x$ on the first day. At the same time, it decreased by 20 m, hence $0.1 x=20, x=200$.