# Are there seven consecutive annual dates which result in Monday-Sunday?

Choose a date that's a Monday, e.g. 1st Jan 2024. Then keep adding 1 year until you have seven dates in a row that are the days of the week in order (Monday to Sunday).

Does such a date combination exist?

Yes

The day of the week will either increase by 1 or 2 when adding a full year, since 365 mod 7 = 1 and for leap years, 366 mod 7 = 2

So

We need 7 consecutive years which do not contain a leap year. A rule for leap years is that if the year is divisible by 100 and not divisible by 400, the leap year is 'skipped'. E.g. The year 2000 was a leap year, but the years 1700, 1800, and 1900 were not.

Example sequence:

Monday, April 1st 2097
Tuesday, April 1st 2098
Wednesday, April 1st 2099
Thursday, April 1st 2100
Friday, April 1st 2101
Saturday, April 1st 2102
Sunday, April 1st 2103

• Trivia: Conventionally, 1700 is a leap year. This is because the majority of the world only switched to Gregorian calendar from Julian after that.
– iBug
Commented Feb 3, 2023 at 4:50
• "Give us back our 11 days!" In Britain (and her dominions), the calendars were aligned to cancel out the accumulated discrepancy. There were no days between 2nd and 14th September 1752. Commented Feb 4, 2023 at 14:00