A palindrome is a sequence of symbols or elements that is the same backwards as forwards. The most famous word palindrome is about Napoleon: Able was I ere I saw Elba. The rules are flexible: You can ignore capitals and punctuation.
Number palindromes are less famous but actually more interesting. There was quite a fuss about the date 11/11/11, which is a rare (once per century) transatlantic palindromic date; a date which is the same in the American and Continental styles.
Six-Digit Palindromic Dates
When we use just the last two digits for the year, palindromic dates obviously repeat every century. The middle two numbers have to be the same: the day in America and the month in Europe. Six-digit American palindromic dates must be on the 11th or 22nd of the month. The month can be from 01 to 12, so there are 24 palindromic dates per century.
In Europe, only November qualifies for the middle two digits, and there is a palindromic date for each day in November in each century. That gives Europeans 30 palindromic dates per century compared to only 24 for Americans.
Eight-digit Palindromic Dates
More interesting are dates expressed with four digits for the year. When we use four digits to express the year, there is a palindromic date for every day of the year between the years 0001 and 9999. With 366 dates (yes, Feb. 29 will be a palindrome in the ninety-third century), there is an average of three and two-thirds eight-digit palindromic dates per century, but they are not evenly apportioned.
We’re fortunate — if you like palindromic dates — to live in a century with 12 of them (American style). Each of the first three centuries of every millennium has twelve; then there are none for 700 years!
The Europeans are even less egalitarian, but they still get more dates. Every day in February is a palindrome in the first two centuries, then none for 800 years!
Celebrating a Palindromic Birthday
Everyone has a palindromic birthday — the exact date on which his/her birthday is a palindrome. My birthday is April 7, so my American palindromic birthday is 04/07/7040. I doubt I’ll be there to celebrate. The odds of being alive on one’s palindromic birthday are about one in one hundred and twenty. My grandson’s birthday is December 2, so he will be 17 on 12/02/2021, and will share a palindromic birthday with Britney Spears.
Much rarer is to be born on one’s palindromic birthday. The probability of that is about one in three million.
Palindromic Dates Past and Future
In America, there have been three palindromic dates since the year 2000 (10/02/2001, 01/02/2010, and 11/02/2011). Before that the last palindromic date was August 31, 1380. The next palindromic date will be 02/02/2020 and the one after that, 12/02/2021: My grandson’s 17th birthday.
Palindromes and Leap Years
Those born on February 29 get cheated out of three out of every four birthdays. However, 9220 will be a leap year, so those born on February 29 will get the same quota (one) of palindromic birthdays as everyone else.
What’s Your Palindromic Birthday?
If you want to figure out your palindromic birthday, just write out your birth month and birth day – then write them again in reverse order. When the numbers read the same from back-to-front as they do front-to-back, you’ve found your birthday’s palindrome. Will you be around to blow out candles?