🔁Which years have the same calendar?

Try one of these too

The identity of a year, in two columns

That table is the whole problem in one view. Ignore the date column — it is New Year’s Day every time — and read the two columns after it. Any two rows whose weekday and leap status both match have identical calendars, from the first Monday in January to the last Sunday in December.

Fourteen rows is exactly the right number to show, because fourteen is all there is.

There are only fourteen possible years

Seven weekdays for 1 January to fall on, multiplied by two states of the leap-year switch, gives fourteen distinct calendars. Every year that has ever been printed and every year that ever will be is one of those fourteen, which is why the puzzle has an answer at all.

They are not equally common. In a 400-year Gregorian cycle, 303 of the years are common and 97 are leap, so each of the seven common-year calendars turns up roughly 43 times and each leap-year calendar only about 14. That imbalance is why a common year finds its twin within a decade and a leap year can wait a working lifetime.

What a repeated calendar is actually good for

Reusing the paper. A wall calendar, a desk diary or a printed year planner from a matching year is correct in every square, and antique calendars are collected and resold on exactly this basis.

Planning by weekday. Shift rotas, cleaning schedules, class timetables and delivery rounds are written against weekdays rather than dates. A matching year lets you lift last time’s plan wholesale instead of rebuilding it.

Checking a historical date. If a document says “Tuesday 14 June” and you know roughly which decade it comes from, the weekday narrows the year down to a handful of candidates — and the finder gives you those candidates in one step.

Sanity-checking a spreadsheet. If a formula insists a date falls on a different weekday than a matching year did, the formula is wrong, not the calendar.

Where the trick stops working

Before 1583. The Gregorian calendar begins in October 1582 and the finder starts the year after, which is not pedantry: the ten days from 5 to 14 October 1582 do not exist in it, so no arithmetic spans that month cleanly.

Across a country’s own adoption date. Britain and its colonies did not switch until September 1752, Russia not until 1918 and Greece not until 1923. A weekday computed on the Gregorian rule for a British document from 1700 will not match the date written on it, because the writer was using a different calendar entirely.

Across 2100, 2200 and 2300. Those century years are not leap years, and each of them breaks the 28-year rhythm for anything reaching across it.

For anything set by the moon. The weekday grid repeats; Easter and the feasts hanging off it do not, and neither do Passover, Ramadan or Chinese New Year. That single exception is what makes a reused calendar nearly right rather than right.

For the rest of the year’s shape — week numbers, leap years and weekday finding — see the calendar tools group; for the dates that shift under their own rules, the holiday dates group, including observed holiday dates and the clock change dates. To measure the gap between two of the matching years directly, use days between dates.