The one-hour sentence -- Valentine's Day and Monday
I was simply trying to write this sentence for the print edition: "Valentine's Day falls on a Monday every ___ or ____ years."
Then I fell into a rabbit hole.
I think I have the right answer now but it took me MUCH LONGER to retrieve it than I should have. (Of course, if you're really smart, you could figure it out without consulting a reference at all.) That's a bad habit -- I can pick at a loose thread until the whole blanket's unraveled.
How many years are there between Monday Valentine's Days?
Show your work, and GO!
Eric was right, in general, Valentine's Day will bounce back in five or six years, depending on whether there are one or two leap years in between. But leave it to OMG...!
Yes, when Valentine's falls on a Monday in the year before a Leap Year, it takes 11 years before Valentines falls on a Monday again.
2012 -- Tuesday
2013 -- Thursday
2014 -- Friday
2015 -- Saturday
2016 -- Sunday
2017 -- Tuesday
2018 -- Wednesday
2019 -- Thursday
2020 -- Friday
2021 -- Saturday
2022 -- Monday
Comments
Should be about every 6 years. The rule is that each day falls one day later in the week every year. ie ifts a Monday this year, it will be a Tuesday next year. But leap year, which comes every 4 years makes it skip one. So instead of once every 7, its about once every 6.
Posted by: vudean | February 4, 2011 4:19 PM
5 or 6, depending upon whether there are one or two leap years between the years in which VD falls on a Monday.
Posted by: Eric | February 4, 2011 4:27 PM
Eric, you're warm....but...
Posted by: The Valentine Kid | February 4, 2011 4:47 PM
In the long run it will converge to once every 7 years.
Posted by: B>) | February 4, 2011 5:17 PM
Because 4 is not evenly divisible into 7, Monday will be skipped over in as many years as it is skipped ahead to.
Posted by: B>) | February 4, 2011 5:28 PM
Well, I do know that Valentine's Day last fell on a Monday in 2005...
Posted by: CherylPR | February 4, 2011 5:40 PM
Beer me, @HitandRunKitty, and let's turn this mother out.
365/7 = 52 weeks + 1 day (52.17)
Leap year = 366 => 52 weeks + 2 days
2011 = non-leap year
2012 = leap year (*)
Note: leap years are divisible by 4
Let 1 = Monday, 2 = Tues, etc.
2011 = 1
*2012 = 2
2013 = 4 (the extra day of leap yr comes after VD)
2014 = 5
2015 = 6
*2016 = 7
2017 = 2
2018 = 3
2019 = 4
*2020 = 5
2021 = 7
2022 = 1
2023 = 2
*2024 = 3
2025 = 5
2026 = 6
2027 = 7
*2028 = 1
2029 = 3
2030 = 4
2031 = 5
*2032 = 6
2033 = 1
2034 = 2
2035 = 3
*2036 = 4
2037 = 6
2038 = 7
2039 = 1
*2040 = 2
2041 = 4
2042 = 5
2043 = 6
*2044 = 7
2045 = 2
2046 = 3
2047 = 4
*2048 = 5
2049 = 7
2050 = 1
Posted by: Owl Meat Geek | February 4, 2011 5:53 PM
So in the coming 40 years the next Monday VDs will be in 11, 6, 5, 6, and 11 years. I continued the series and it is:
11, 6, 5, 6, 11, 6, 5, 6 ...
That's obviously a repeating series, so the correct sentence would be:
"Valentine's Day falls on a Monday every 5, 6 or 11 years."
Proof that 7 is the average, although not the expected value or even a valid value:
(11 + 5 + 6 + 6) / 4 = 7
By extension this rule can be applied to any fixed annual event, such as Christmas or birthdays.
Naps make you smarter
Posted by: Owl Meat Garanimal | February 4, 2011 6:36 PM
Eric would have been right if he had said the next VD Monday will be in 5 and/or 6 years. that covers all possibles. The repeating sequence 11, 6, 5, 6 ... seems odd and inelegant until you realize that 11 is the sum of 5 and 6.
Always seeking deeper meaning ... (also kind of zippy from the coffee/cocoa/pumpkin pie spice drink I just made. )
Posted by: Owl Meat FibonachosSequence | February 5, 2011 11:18 AM
In the long run it will converge to once every 7 years.
In the long run we're all dead.
Posted by: John Maynard Keynes of Cross Keys | February 5, 2011 4:17 PM