Given the historic nature of this year's presidential inauguration, I was wondering: can the inauguration take place on MLK day?

Since Martin Luther King Day occurs on the third Monday of January, it is possible for this day to be January 20. However, since MLK Day is a federal holiday, would an inauguration take place on that day if the two dates coincided?

Using a perpetual calendar, I've found that, in 2025, MLK Day will be on Jan. 20. This would be the scheduled inauguration day for the 2024 presidential election. This was also the case in 1997. What happens?