A certain notation will have to be agreed at the outset :
6th March 2001 will be 06/3/01 rather than 6/3/1 or 06/03/01. This prevents the problem
becoming too trivial, and does fit with most of our day to day usage, I think.
The choice is whether to begin by looking at each year, to see how many eligible dates
there are in, for example, 2001, then 2002 and so on, or concentrate on each possible
day of the month ( eg dates that begin with 23/../.. )
The latter seems quicker, as we only have 31 cases to consider, rather than the full 100
for the former method.
Firstly then, considering the month part in the middle, it's clear that October and
December are out of it, and that February will have to be looked at a bit carefully when
we get to the 29th !
So, for each day from the 1st to the 28th, there will be 10 months a year that will fit in, as
long as the Year is the reverse of the Day.
eg 01/../10, 02/../20, ........through to 28/../82 each have 10 possible middle parts. This
gives us 28 x 10 = 280 eligible palindromes, so far.
For the 29th, we have another 10 months, in fact, as 29/2/92 is a leap year date.
For the 30th, we miss February out... only 9 months fit the bill in 2003.
Finally, for the 31st, we have only 5 months in 2013, namely :
31/1/13, 31/3/13, 31/5/13, 31/7/13 and 31/8/13.
This comes to a Grand Total of 304 dates per century, or 3040 per Millennium !