Overview of Leap Years with February 29 on Saturdays

February 29th falls on a Saturday in select leap years, creating a pattern that can be memorized and predicted. This article delves into the frequency of this occurrence, providing insight into its mathematical and calendrical basis.

The Pattern of Leap Years

February 29th falls on a Saturday in the following leap years:

1968 1992 2020

The next occurrence will be in 2048. Leap years, which include February 29, occur every 4 years, with exceptions for years divisible by 100, unless they are also divisible by 400.

Mathematical Insight for Memorization

In 1965, I devised a memorization system to identify leap years where February 29 falls on a Saturday. My method leverages a 28-year cycle. Although a complete cycle every 28 years is typical, the year 2000 was an exception because it was divisible by 400 and thus not a leap year.

To determine the previous leap year when February 29 fell on a Saturday, subtract 28 years from the current year. For instance:

2020 - 28 1992

Therefore, 1992 was the last time February 29 landed on a Saturday.

Calendar Repeating Patterns

Calendars repeat every 28 years, meaning the 2020 calendar is identical to that of 2048 and 1992. This pattern can be applied to any year between 1904 and 2096. While 1900 and 2100 are not leap years, this 28-year cycle doesn't apply to them.

Throughout my lifetime, I encountered this phenomenon three times: in 1964, 1992, and 2020. It's likely that I won't be around for the next one, which will occur in 2048.

Further Insights into Leap Years

Leap years following a specific pattern can also result in February 29 falling on a Sunday. These years have a unique starting day of the week.

Examples of Leap Years Starting on Thursday: 1948, 1976, 2004, 2032

In every 400-year cycle, 13 leap years will begin on a Thursday, making a total of 97 leap years within that cycle.

Using Perpetual Calendar Apps

Perpetual calendar apps treat January and February as months 13 and 14 of the previous year, making the question equivalent to finding March 1 of a leap year on Sunday. By checking a perpetual calendar app:

1620 1648 1676 1716 1744 1772 1812 1840 1868 1896 1908 1936 1964 1992

Note that the Gregorian calendar has a 400-year cycle for exact repetition, and within each century, there's a 28-year cycle, but this cycle doesn't carry over into century years that are not leap years.