Palindrome Date Finder

What Is a Palindrome Date?

A palindrome is any sequence that reads the same forwards and backwards: “racecar”, “madam”, “level”. A palindrome date is a calendar date that, once you strip the separators, forms a palindromic string of digits. February 2, 2020 written as 02/02/2020 becomes 02022020, and reversed it is still 02022020.

Why Are They So Rare?

Write an eight-digit date as M₁M₂D₁D₂Y₁Y₂Y₃Y₄. Being a palindrome forces four pairings at once: M₁=Y₄, M₂=Y₃, D₁=Y₂, D₂=Y₁.

Look at what that does in our century. Every year from 2000 to 2099 starts with the digits 2 and 0, so Y₁=2 and Y₂=0. The pairings immediately fix the day at 02 and leave you no choice about it. The month is then the year’s last two digits read backwards. Almost every year produces an impossible month, and the handful that survive are the entire list.

The 20th century produced zero in this format, for the same reason. Years 19xx force the day to be “91”, which is not a day.

Every MM/DD/YYYY Palindrome Date This Century

There are exactly 12, and here they all are:

Notice that every single one falls on the 2nd of the month. That is not a coincidence, it is the constraint above doing its work.

Format Differences Matter Enormously

This is where most articles on the subject get it backwards.

The European DD/MM/YYYY format wins, and it is not close: 29 palindrome dates this century against 12. The reason is that DD/MM/YYYY pins the month to 02 rather than the day, and February has 28 or 29 candidate days to offer where a month slot only has 12. So European readers get 02/01/2010, 02/11/2011, 02/21/2012, all the way out to 02/29/2092, which needs 2092 to be a leap year and, happily, it is.

The ISO YYYY-MM-DD format produces exactly the same 12 dates as the US format. Work the pairings through and ISO forces day=02 and month=(year backwards), which is the identical constraint. Different-looking format, identical answer. If you have read somewhere that ISO yields more palindromes, it does not.

Only one date this century reads as a palindrome in all three formats at once: 02/02/2020. Anyone who noticed at the time was noticing something genuinely rare, and the next all-format repeat is 03/03/3030.