Environmentalists have protested against the large volume of logging. The chairman of the forestry company calmed them down as follows: "In the forest, $99\%$ are pines. Only pines will be cut, and after the logging, the percentage of pines will remain almost unchanged - pines will be 98\%". What part of the forest is designated for logging?
The number of "non-pines" remains constant, while the proportion of "non-pines" increased from one percent to two...

## Solution

We will call trees that are not pines oaks. Before the logging, oaks made up $1 \%$ of all trees, and after logging, they will make up $2 \%$. This means that the total number of trees will be halved.

## Answer

Half.

What is the maximum number of Fridays that can be in a year?

## Hint

Start the week with the day of the week on which January 1st falls in the year in question, in which case there is still one Friday per week.

## Solution

We will assume that the week starts on the day of the week on which January 1st falls in the year in question (i.e., if January 1st is a Wednesday, then we consider the week to start on Wednesday and end on Tuesday). Then, from the beginning of the year, [365/7]=52 ([366/7]=52 in a leap year) full weeks pass, each of which has exactly one Friday. In addition, at the end of the year, there are still $365-7 * 52=1$ or $366-7 * 52=2$ days left. We can provide an example (take one of the recent years) when one of the remaining days is a Friday. In this year, the maximum possible number of Fridays - 53 - is achieved.

## Answer

53.00