How often do calendars repeat? [Travel day Filler]

Okay, this is not an interesting photo, but what it caused was interesting.

This is the travel alarm clock among the three recently posted that takes a common battery, so I put a battery in to see if I could set it up and possibly give it away. Well, set-up was interesting! Not only does one set the time and the time zone, but also the date. However, 2024 was not an option for the year; the clock would only accept a year up to 2019. So then I wondered, “Hmm. Is there a year it will accept that corresponds to 2024?” Short answer, Yes, but…

The investigation led me back to an Excel spreadsheet I set up a few weeks ago when we came across a Shutterfly calendar from 2019: the card for each month had Grandchild #1 photos on it … but the individual cards or months did not have the year printed on them. At the time, I determined that the 2019 calendar would not repeat until 2030 (in 11 years). What about matching 2024 on a clock going only as far as 2019?

There are several years the clock would accept that would match the 2024 calendar: 2001, 2007, 2018. Unfortunately, while 2024 is a leap year, none of those other years is a leap year, so when the clock cycled over to the next year (2002, 2008, 2019), it would not match next year, 2025.

So how many years between calendar years that match and will match in succeeding years as well? Twenty-eight. So the 2024 calendar will not line up with another calendar until 2052. (And the last, earlier year that would align would be 1996.)

This is not surprising.
     » Days-of-the-week run in cycles of 7.
     » Leap years run in cycles of 4.
And 7 × 4 = 28. Voila!

This year, January 1 fell on a Monday. That will happen again in 5 years (2029), another 6 years (2035), another 11 years (2046), and finally another 6 years (2052). That’s the cycle of repeating calendars: 5 / 6 / 11 / 6. Aren’t you glad you read this far? Sorry!

You know the rule, yes? With no leap year involved, today’s date falls on the following day-of-the-week next year. Then:
    January 1, 2024: Monday
    January 1, 2025: Wednesday (because 2024 is a leap year with a February 29)
    January 1, 2026: Thursday
    January 1, 2027: Friday
    January 1, 2028: Saturday
    January 1, 2029: Monday (skipping a day because 2028 is a leap year).

Why is this so? With 7 days in a week and 365 days in a non-leap year, 365 ≡ 1 (mod 7).
» Modular arithmetic at Wikipedia

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February 13 posts
  1 year ago: “‘Wet launch’: Brrrr!”
2 years ago: No post
3 years ago: “Infusion”
4 years ago: “Trying a new shower head”
5 years ago: No post
6 years ago: “Candlestick redux”
7 years ago: “I hope they weld-and-toe better than they spell-check…”
8 years ago: “Cristaudo’s Pink cookies”
9 years ago: “Maranta, perhaps?”
10 years ago: “This was too easy!”
11 years ago: “Spathiphyllum”
12 years ago: “That does not compute.”
13 years ago: “Valentine’s Day Eve”

13th February 2024 13th Feb 24