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For those too young or unlucky to pick up the reference, parent is referring to Car Talk, a radio show featuring Tom and Ray Magliozzi and their live solutions to automotive problems (also, existential life questions).

After running for decades, it was finally retired in 2012. The archives remain, in my opinion, some of the finest exercises in logical problem solving.

http://www.cartalk.com/

For better or worse the show is still airing "best of" episodes. I hear the end of it every Saturday morning when I switch to my local NPR station to hear the show that comes on after it.

Well this story did show up on Car Talk as a puzzler in 1997:

http://web.archive.org/web/20030814220711/http://cartalk.car...

http://www.snopes.com/autos/techno/icecream.asp

Hope this doesn't ruin it for you, but I knew someone who had a problem presented on the show. She called in and reached an answering machine. Someone called her and qualified the problem. Then one of the brothers called and talked to her for a while. Then a few weeks later (there might have been some more calls, I don't know) both brothers called her and talked to her for a while. Her parts of that last call was edited into the radio show so it sounded like she had called and they just figured out the answer on the spot.