1.1. If the 200th day of some year is Sunday and the 100th day of the following year is also Sunday, then what day of the week was the 300th day of the previous year? Enter the number of this day of the week (if Monday, then 1, if Tuesday, then 2, etc.).
Answer. 1.

Solution. Between the $200-\mathrm{th}$ day of the year and the $100-\mathrm{th}$ day of the next year, there are either $165+100=265$ or $166+100=266$ days. The number 266 is divisible by 7, while the number $265-$ is not. Therefore, the current year has 366 days, meaning it is a leap year. Thus, the previous year was a common year. Therefore, between the $300-\mathrm{th}$ day of the previous year and the $200-\mathrm{th}$ day of the current year, there are $65+200=265$ days. Since $265=7 \cdot 37+6$, the number of days is 1 less than a multiple of 7. Therefore, it was a Monday.