On Saturdays, I like to lay about in the forenoon, drinking coffee, maybe roughhousing with the girls, and then, at 11:00, tuning into "Car Talk" on NPR. Not that I care about cars. I'm the kind of coffee-shop loitering, Obama-voting, public transportation-using urban liberal who, in my bachelor days, contemplated going car-less. But then how would I get myself and my golf clubs to whatever course my friends were playing this weekend? Plus, I had to travel forty miles each way on the big holidays. So year in and year out I would drive 6000 miles, first in a Dodge Omni, then in another Dodge Omni, then in a Toyota Tercel that one of the regulars in our golf foursomes, the owner of a Suburban, nicknamed "Big Blue."
I remember the first time I tuned into "Car Talk." It was an accident. I'd been listening to something else, and by the time this crazy car call-in show came on I was washing dishes and so didn't click off the radio. The first caller was a woman with some car trouble, I can't remember what, that she described in considerable detail. When she finally came to the end of the symptoms, one of the hosts asked: "What color is the car?" I kept listening and soon was hooked.
Like other fans of the show I remember favorite calls. One day Senator Tom Harkin called in with a car question. I like the genre of calls involving women seeking an impartial adjudication of a car argument they've been having with the husband or boyfriend. It's pretty clear to me that men, since they feel obliged to have an opinion on a car question, are more apt to be wrong than women, who are free to have no opinion and therefore only express one when they have an actual reason for believing as they do. My favorite call of all time was probably the one in which the fellow's dog had gotten car sick and ralphed onto the dash, so that the puke seeped into the heat register, with the result that every time he ran the heater the car smelled of dog vomit. They had a lot fun with that one, and finally advised the caller to sell the car--in the summertime. They have a lot of fun with almost everyone before finally dispensing what I assume is consistently good advice.
I also like "the puzzler," a regular feature that is as often mathematical as auto-related. (An ongoing good-natured joke concerns the utility of math and science over and against "the humanities"; whenever someone calls in and says they are a student, inquiries concerning their field of study are sure to follow, and an answer like "art history" or "comparative literature" elicits loud groans. Of course they have no clue what to do about their problematic vehicles!) Since I haven't placed a post in my "Math" category for awhile, let me give an example of a recent Car Talk Puzzler.
There are three scraps of paper, each with a different number written on it. You have to pick the one that has the biggest number. If you want, you can look at one and then decide whether or not to choose it. If you decide not to choose it, that one is out: you have to choose one of the other two. If you look at one of the remaining ones, you must either choose it or the last one. The question is: What's the best strategy? It's obvious that just guessing at the start of the game gives you a one-third chance of winning. Can you do better than that?
Yes, you can. The best strategy, it turns out, is to look at one paper but never choose it. Then, if the second paper has a higher number than the first, keep it; but if it has a lower number reject it also and make the third your choice. Here is the way to analyse it. There are only six orders in which the three papers may be chosen. Let us denote the papers 1, 2, and 3, where 1 stands for the paper with the smallest number and 3 for the one with the biggest. The six possibilities are:
i. 1, 2, 3
ii. 1, 3, 2
iii. 2, 1, 3
iv. 2, 3, 1
v. 3, 1, 2
vi. 3, 2, 1
Each sequence is as likely as another to represent the order in which you choose them. In (i.) you lose, because you end up with (2), not (3). In (ii.), you win. Scenarios (v.) and (vi.) are both losers but (iii.) and (iv.) are both winners. That's three out of six winners, which is a fifty percent improvement over just guessing at the start of the game. (Uncovering first one and then another but always settling on number three is the same as just guessing that three is the highest without turning any over.)
An archive of "Car Talk" puzzlers is here. The one I've described was for February 12 of this year.
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