## Task B-2.3.

One year, January 1 and April 1 were both on a Thursday. How many months in that year have five Fridays? Justify your answer.
## First solution.

From January 1 to April 1, there are 90 or 91 days. Since both dates fell on the same day, the number of days between them must be divisible by 7.

Therefore, there are 91 days between them, indicating a leap year.

A leap year has 52 weeks and 2 days. January 1 was a Thursday, which means January 2 was a Friday, and there were 53 Fridays in that year.

In one month, there are either 4 or 5 Fridays. Let \( n \) be the number of months with 5 Fridays. Then,

$$
5 n + 4(12 - n) = 53, \quad \text{that is} \quad n = 5.
$$

2 points

We conclude that there were 5 months with 5 Fridays (January, April, July, October, and December).

1 point