### Timing

These two challenges will test your time-keeping!

### Millennium Man

Liitle Millennium Man was born on Saturday 1st January 2000 and he will retire on the first Saturday 1st January that occurs after his 60th birthday. How old will he be when he retires?

### Calendar Sorting

The pages of my calendar have got mixed up. Can you sort them out?

# Palindromic Date

##### Stage: 2 Challenge Level:

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
:
: