WWTBAM Bored

Sometime in the 21st century, the following conversation takes place:

“Don’t throw out that calendar! You could reuse it in the future, when the days and dates on the calendar match up again.”

“OK, but that won’t happen for a long time. Forty years, in fact.”

“You’re right! In fact, this calendar has never had a 40-year gap before.”

What year is it?

So just going by my knowledge of when Leap Day will occur in the years that have it, I was able to determine that there are five calendars that will take an extra long 40 year leap before they are repeated....

2072 (Mon 2/29) next in 2112
2076 (Sat 2/29) next in 2116
2080 (Thu 2/29) next in 2120
2084 (Tue 2/29) next in 2124
2088 (Sun 2/29) next in 2128

2092 and 2096 will only take 12 years to cycle back around (rather than the usual 28) due to the 8 year gap in leap years.

So the last part of the problem (this calendar has never had a 40-year gap before) must want to pare down those five possibilities to one based on the handful of previous times a century non-leap year happened...

Well, since 1904 had a Monday Leap Day, Saturday (for 1908) would have also has a 12 year gap, leaving the other five days having the 40 year gap around 1900. So we're down to just Monday (2072) and Saturday (2076)...

1804 would have been a Saturday Leap Day, with its 12 year pair being Thursday (1808).... so that leaves just Saturday for 2076!

One more anomaly to check. America adopted the Gregorian calendar in 1752 (via England), with 11 days being removed from the calendar that September (I believe the days of the week were kept intact and only the dates were shaved)....

So.... 1796 had a Thursday 2/29 (The same as 1996!) giving us 1768 (Thu), 1764 (Sat), 1760 (Mon), and Wednesday in 1756. The expected 2/29 in 1752 would have been Friday, but with the correction, instead it was a Monday. So we have....

1752 & 1760 for Monday, 1748 & 1756 for Wednesday.... the others would all have the same unusually long gap. Saturday would be 1728 and 1764.... 36 years apart. Not quite 40!

So, based on the American version of the Gregorian calendar.... the last possible leap year calendar to not have a 40 year gap will be the one that occurs in 2076, Final Answer!

That's ASSuming I didn't screw up any of my math (No, I consulted no perpetual calendars for this exercise)....

Another reason to look forward to the tricentennial.