Twosday

I was curious the other day and wondered if 2/2/2 was a Tuesday. A Tuesday Twosday eh? I plugged the date into a calculator and was mildly disappointed to learn that it was a Thursday.

But there were many other dates to check, so I continued:

2/22/2	Wednesday
2/2/22	Monday
2/22/22	Sunday
2/2/222	Saturday
2/22/222	Friday

That’s it for the past! Just how far in the future do we have to wait for a Tuesday Twosday!?

2/2/2222	Saturday
2/22/2222	Friday
2/2/22222	Saturday
2/22/22222	Friday

Hold on, now we’re just repeating ourselves. But will it repeat forever?

Normally the day of week for any given day of the month progresses by 1 every year, except on leap years when it progresses by two. We’ll have a leap year every four years, unless the year is divisible by 100, unless unless the year is divisible by 400.

The Gregorian calendar cycle lasts 400 years. This gives us a total of 400 (base) + 97 (leap) = 497 day-of-week-progressions per Gregorian cycle. 497 divided by 7 is a round 71 – the cycle loops back to the same day of week!

Alas, as we continue our search for Twosdays we will always add multiples of 400 years to the date, and the day-of-the-week for our Twosdays will remain forever Saturday and Friday.

It amuses me that we’ve seen every other day-of-the-week get its own Twosday – go figure!

There’s more to the story though; as luck would turn out 2/2/2022 was a Tuesday! Many people celebrated that as Twosday and who knows, maybe everyone’ll come back in four hundred years for round two! ; )