Have you ever heard of a palindrome? It’s a word, phrase, sentence (or more) that’s spelled exactly the same way backward and forward. Here are a few well known palindromes:

- race car
- A man, a plan, a canal, Panama!
- I prefer pi
- Dammit, I’m mad!
- Ma is as selfless as I am
- Never odd or even

Today we’re going to talk about palindromic dates, which I’ll define for you right now. If we write any date using the format MMDDYYYY, we get a string of eight digits (for example, today’s date would be written “04082011″). A palindromic date is any date for which the eight digit string looks the same whether written backward or forward.

Today’s date is *not* a palindrome because “04082011″ is not the same as “11028040″. How about this one: January 2, 2010? Is that a palindrome? Let’s see…written forward that would be “01022010″ and written backward it would be “01022010″. Yup, that’s a palindrome. Got it? Ok, now you’re ready for today’s challenge: ** Tell me the most recent palindromic date before January 2, 2010.** Extra credit if you can give me the

*two*most recent palindromic dates before 01/02/2010. You know the drill – leave your answer in a comment below.

By the way, there’s also a concept of a word level palindrome, where if you reverse a sequence of words, you end up with the same sequence of words you started with. Here are a few cute examples (none of which are original):

- King, are you glad you are king?
- Says Mom, “What do you do?” – You do what Mom says.
- You know, I did little for you, for little did I know you.
- Please me by standing by me please.
- Blessed are they that believe that they are blessed.
- Escher, drawing hands, drew hands drawing Escher.

That last one blows my mind. Have a nice weekend. :)

**Solution:** Let’s work our way backward, in years, from 2010. 2009 doesn’t work because when written backwards it gives us an invalid month (90). Same story for 2008 through 2002 (month numbers 80, 70, …, 20). But 2001 gives us both a valid month (10) and day of month (02). That gives us the first answer: October 2, 2001 (10022001) is the most recent palindromic date before 01/02/2010.

Continuing backwards, 2000 gives us an invalid month (00) so that year is out. All of the 1900s are out because they imply an invalid day of month (91). Ditto the 1800s, 1700, 1600s, 1500s and 1400s. Finally, we come to the 1300s, which implies a valid day of month (31). 1399 through 1391 again give invalid months but 1390 gives us a a valid month (09) and a valid day of month (31). Alas, although September 31, 1390 (09311390) is palindromic, September has only 30 days! Back to the drawing board…1389 through 1381 yield invalid month numbers but 1380 gives us a valid month (08) and a valid day of month (31). Let’s see – that would be August 31, 1380 (08311380). Yup, that’s a palindrome and a valid date. That’s our second answer.

So the most recent palindromic date before January 2, 2010 occurred less than ten years ago. Amazingly, the next most recent palindromic date occurred over 600 years ago. Congrats to Ricardo Agudo, Katy Gustafson, Al Pessot, Lalo Hidalgo and John Holland for correct answers!

08/31/1380

07/31/1370

10 02 2001

12 13 3121

oops – bad typo

12 31 1321 is what I meant

OK – trying again

10 02 20 01

08 31 13 80

Since the 1st 2 digits are the month, they must be between 01 and 12.

Take 2010 and go back until the last 2 digits when flipped create a valid month.

2009 makes month 90 which is invalid. 2001 givens a month of 10.

10022001, Oct 2, 2001 is the most recent palindromic date.

Continuing with the same process, the next year that produces a valid month

would be 1921, 2112, 12911921, but there is no 91st day of december.

The first valid day is 31, which gives us a year in the 1300s.

So we’ve got xy3113yx. Since december is the last month of the year with 31 days,

we end up with 12311321, Dec 31, 1321 as the 2nd most recent palindromic date.