Task 5.1. In a certain month of a certain year, there are exactly 5 Fridays. At the same time, the first and last day of this month are not Fridays. What day of the week is the 12th day of the month?
Answer: Monday.

Solution. Let's consider all possible options for what day of the week the 1st of the month could be.

Suppose the first day of this month is Monday. Then the Fridays are the 5th, 12th, 19th, and 26th. There are only four - this does not fit us.

Suppose the first day of this month is Tuesday. Then the Fridays are the 4th, 11th, 18th, and 25th. There are only four - this does not fit us.

Suppose the first day of this month is Wednesday. Then the Fridays are the 3rd, 10th, 17th, 24th, and 31st. There are five, but Friday is the last day of the month. This does not fit us again. Suppose the first day of this month is Thursday. Then the Fridays are the 2nd, 9th, 16th, 23rd, and 30th. This fits if the month has 31 days. And in this case, it turns out that the 12th is a Monday.

The first day cannot be a Friday.

Suppose the first day of this month is Saturday. Then the Fridays are the 7th, 14th, 21st, and 28th. There are only four - this does not fit us.

Suppose the first day of this month is Sunday. Then the Fridays are the 6th, 13th, 20th, and 27th. There are only four - this does not fit us.