Palindromic Date

Lots of solutions to this problem were submitted this month.

Clement from River Valley High School and Andrei of School 205, Bucharest, sent in the most complete solutions, with Andrei explaining his method clearly and Clement looking at the time between the dates. Clement's findings were very interesting it would be good to try to explain why the patterns of time between palindromic dates is as Clement describes. When you identify patterns in investigations and problems like this it is very useful to identify why the pattern works in terms of the mathematical problem or context itself.

Below is a solution based on Clement's and Andrei's work.

I used the listing method to solve this question.
My results are as below:

I observed that the palindromic date in February written in the British way is:
dd/mm/yyyy

where mm and yyyy are 02 and 2002 respectively:
dd/02/2002

It is read from left to right:
dd022002

This date must be read in the same manner from right to left:
200220dd

So, in February dd is 20 and the date is:
20/02/2002

I searched only for dates from this century:
dd/mm/20yy

and the date read from right to left:
dd/02/yyyy

So, this century all palindromic dates written in the British way are in February. Now, in search for other palindromic dates in this decade:
30/02/2003

But, this date does not exist and from now on the days will be 40, 50 etc. and these dates do NOT exist. So, I found the following date in 2010 :
01/02/2010

Now, I wrote the solutions in the following table:

Then I searched for palindromic dates in this century in the American way:
mm/dd/20yy

and
mm/02/yyyy

The month may be 01, 02, 03,?, 12:

Days between the Palindromic Date for British & American ways:

For British way, if first year is 20/02/2002:

-19 days + 8 years
+ 10 days + 1year
+ 10 days + 1year
-19 days + 8 years
:
:

For American way, if first year is 01/02/2010:

+ 10 days + 1 year
- 9 days + 9 years
:
:

03/02/2030 then:

+ 1 day + 10 years
:
: