Save those number candles

My mom emailed me yesterday to share this factoid with me on the eve of her 63rd birthday:

This is the last day when you will be 26 and I will be 62, when our ages are mirror images.  It might happen again in eleven years (for three months) when you are 37 and I am 73, assuming we both live that long.  We'll probably both have white hair by then.  Incidentally, you were born in '84 and I was born in '48, so we've been mixing up the numbers for a long time.

Have a nice day!

Love, Mummy

Assuming I live to be 37?! Really, Mommer? Li'l dark.  And nice dig about the hair... But then she went on in a second email about half an hour later:

Now I really can't tell you why this is true, but this is actually the third time our ages have been mirror images -- when you were 04 I was 40, when you were 15 I was 51.

We've already done the 26-62 and 37-73 ones, but it will happen again at 48-84 and then 59-95, but then it stops.  

The Internet tells us that palindromic ages, when they occur, always happen every 11 years, and the age difference has to be a multiple of 9 (i.e. 4 x 9 = 36, the age difference between us).  The difference between the digits will always be the factor for the nine (i.e. 6 - 2 = 4; 5 - 1 = 4).  

But why, I can't tell you.

She has since been signing her emails to me: "2662!"  Can we say adorable? All together now!

Happy Birthday, Mom! I've been mirroring you in some ways my whole life -- remember those purple sweatsuits? :) I love you very much - have a wonderful day and see you tomorrow for lobbies!