Can there be a month with 6 Mondays? (or 6 of any other days?)

Question

This year, this month (November) we've 5 Mondays so I get 5 pay checks on 2nd, 9th, 15th, 22nd, 29th (which feels very good - I get paid one extra check :-).

I wonder if it's possible some years to have 6 Mondays? I haven't seen it but I wonder if there will be such year?

If Monday is not possible, then is any other week day possible to happen 6 times in one month?

(I'm mathematics enthusiast, no deep knoweldge - thanks!)

Answer 1

To fit the maximum number of Mondays in a month, you'd want the first day of the month to be a Monday. Then it is easy to see:

• 7 days after that, you have 2 Mondays in your month, total days: 8
• 7 days after that, you have 3 Mondays in your month, total days: 15
• 7 days after that, you have 4 Mondays in your month, total days: 22
• 7 days after that, you have 5 Mondays in your month, total days: 29

The next step would lead to total days: 36, so: No, you can at most have 5 Mondays in a month.

In the above, replace Monday with your favorite day of the week and you'll see Mondays are not alone in this, the same goes for Tuesdays, Wednesdays,Thursdays, Fridays, Saturdays and Sundays.

Answer 2

The longest month has 31 days. The most Monday's that could occur in a month is when Monday is the first day of the month. That would give a Monday on the 1st, 8th, 15th, 22nd, and 29th. So no, the next Monday would occur in the month afterwards.

Answer 3

There are at most 31 days in a month, and a Monday occurs every 7 days. If there were to be 6 Mondays, there would have to be at least 5 gaps of 6 days, which is 30 days. Add that to the 6 Mondays, and you get 36, which is bigger than 31.

Thus, it is not possible to have a month with 6 Mondays.

Answer 4

If the 1st is a Monday, being the most hopeful case, then so are the 8th, 15th, 22nd, 29th and 36th days of the month. The 36th is at least the 5th of the next month.

Answer 5

Well, let's go crooked here. You CAN have 6 Mondays in one month. Go to the Diomede Islands in the Bering Sea, between Russia and Alaska. The International Dateline passes right between the 2 islands. So Big Diomede (on the western side of the IDL) is always one day ahead of Little Diomede (belonging to Alaska). So, as others mentioned, let there be a Monday on the first of the month and you are on Big Diomede. After the 5th Monday it becomes Tuesday the next day, but then you hop on the boat to little Diomede the enjoy (another) Monday. Is it the same 5th Monday? That's a good debate, because YOU has a little Tuesday inbetween.

Answer 6

Mathematically, no it can't.

Practically, however, yes it can.

The calendar is defined by law, and there is precedent for the calendar being changed. In September 1752, Great Britain and the British Empire switched from the Julian to the Gregorian calendar, thereby skipping 3-13 September. This month only had 2 Mondays.

If dates can be removed by a law, they can also be added by law. If a country decided to switch the other way, right now, having already had 4 Mondays this month (today is 27 November 2015, Gregorian), we'd jump back to the 14th, and have two more Mondays (Julian and Gregorian weekdays are the same - Today is Friday the 14th Julian, Friday 27 Gregorian).

The Julian calendar is rarely used now, it drifts relative to the tropical year (that is, the day that the sun crosses the equator mid-autum(fall)/mid-spring keeps moving earlier and earlier).