1. In one year, January 1 and April 1 fell on a Thursday. How many months in that year had 5 Fridays?
Solution. From January 1 to April 1, there are 91 or 90 days, depending on whether the year is a leap year or not. For January 1 and April 1 to be a Thursday, the number of days between these two dates must be divisible by 7, which is the number 91. Therefore, the year is a leap year and has 366 days. Thus, in this year, there are 52 weeks and 2 days, meaning there are 53 Fridays (since January 2 is a Friday). Each month has 4 or 5 Fridays. If we denote the number of months with 5 Fridays by $x$, then $12-x$ is the number of months with 4 Fridays, so $5x + 4(12-x) = 53$, from which we get $x=5$. Therefore, in this year, there are 5 months with 5 Fridays.