1. How many weeks can a year overlap? Assume that a year overlaps with a week if at least 6 and one day of this week falls within the given year.
Answer: On the 53rd 54th week. Solution. If there are 365 days in a year (a non-leap year), then since $365=52 \cdot 7+1$, there are no fewer than 53 weeks in a year. If it is a leap year, meaning there are 366 days in a year ( $366=52 \cdot 7+2$ ), there is a situation where the year starts with the last day of the week, followed by 52 full weeks, and then the first day of the following week - a total of 54 different weeks. If there are 55 (or more) weeks, then there must be no fewer than 53 full weeks, which is impossible, as $53 \cdot 7=371>366$.