Flipping Ages

Mar 31, 2008

RAY: This was sent in many weeks ago by Wendy Gladstone, and as usual I tweaked it a little bit.

She writes: "Recently I had a visit with my mom and we realized that the two digits that make up my age when reversed resulted in her age. For example, if she's 73, I'm 37. We wondered how often this has happened over the years but we got sidetracked with other topics and we never came up with an answer.

"When I got home I figured out that the digits of our ages have been reversible six times so far. I also figured out that if we're lucky it would happen again in a few years, and if we're really lucky it would happen one more time after that. In other words, it would have happened 8 times over all. So the question is, how old am I now?"
RAY: Here's the answer: if you started monkeying around you would figure out that the mother had to be some multiple of nine years old when her child was born. For example take the number 12 and 21, those are certainly palindromic but that would mean the mother was 9 when her daughter was born so that doesn't work.

TOM: Yeah.

RAY: But if the mother was 18 when the child was born, the child would be 02. And then, every 11 years it happens again. If you look at the daughter's age, it goes from two to 13 to 24 to 35 to 46, in each case you're adding 11 years to the daughter's age and it's also doing the same thing to the mother's age, 31, 42, 53, 64, etc., etc. So it turns out that Wendy would be 57, and her mother would be 75. That's the sixth time that it happens.
The next time it happens, she'll be 68 and mom will be 86. And then the next time Wendy will be 79, and mom will be 97. So for them it could happen eight times. Who's our winner?

TOM: The winner is Doug Hoffman from Williston, North Dakota, and for having his answer selected at random from the pile of correct answers that we got, Doug is going to get a 26-dollar gift certificate to the Shameless Commerce Division at cartalk.com, with which he can get a beautiful Save the Skeets T-shirt.

RAY: Get out. Now for those of you who don't know, the Save the Skeets Foundation is our favorite charity, I mean once we found out that people were shooting the poor little things --

TOM: Right, how could we just sit by and let it happen, right? So we started the Save the Skeets Foundation and a Save the Skeets T-shirt is yours, Doug, if you want it.

RAY: And maybe even if you don't want it. Congrats Doug!

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