Palindromic Date
Problem
The number $2002$ is palindromic because it is the same read from left to right as it is read from right to left.
There was one date in February of the year $2002$ where the eight digits are palindromic if the date is written in the British way (dd/mm/yyyy).
This is not palindromic written the American way (mm/dd/yyyy).
Is there any palindromic date written the American way that year?
Find the next occasions when palindromic dates occur written in each way and the number of days between them.
Getting Started
How can this help you?
Student Solutions
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
:
: