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Palindromic Date

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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:

Date
Observation
dd mm yyyy
20 02 2002
30 02 2003 Not a date
01 02 2010
11 02 2011
21 02 2012
31 02 2013 Not a date
02 02 2020
12 02 2021
22 02 2022
32 02 2023 Not a date
03 02 2030
13 02 2031
23 02 2032
33 02 2033 Not a date
04 02 2040
14 02 2041
24 02 2042
34 02 2043 Not a date
05 02 2050
15 02 2051
25 02 2052
35 02 2053 Not a date
06 02 2060
16 02 2061
26 02 2062
36 02 2063 Not a date
07 02 2070
17 02 2071
27 02 2072
08 02 2080
18 02 2081
28 02 2082
09 02 2090
19 02 2091
29 02 2092 Not a date

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:

mm dd yyyy
02 02 2020
03 02 2030
04 02 2040
05 02 2050
06 02 2060
07 02 2070
08 02 2080
09 02 2090
11 02 2011
12 02 2021

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
:
: