Problem 4.7. Vanya goes to the swimming pool every Wednesday and Friday. After one of his visits, he noticed that he had already gone 10 times this month. What will be the date of the third visit in the next month if he continues to go on Wednesdays and Fridays?
Answer: 12.

Solution. Vanya visited the swimming pool 10 times in a month, which means he visited it 5 times on Wednesdays and 5 times on Fridays.

If the first visit to the swimming pool in this month fell on a Friday, then from the first Friday to the last Friday he visited (including the first and last Friday), 29 days have passed. This means that in this month, there are no more than two days left, so the next Wednesday will fall into the next month.

If the first visit to the swimming pool in this month fell on a Wednesday, then from the first Wednesday to the last Wednesday he visited (including the first and last Wednesday), 29 days have passed. In the month, there are no more than two days left, so the last Friday falls exactly on the 31st of the month.

Thus, the Wednesdays in the next month will fall on the 5th, 12th, 19th, and 26th, and the Fridays on the 7th, 14th, 21st, and 28th. The third visit will be on the 12th.