Painting by Numbers

Feb 08, 2010

RAY: This was from my painting by numbers series and it was sent in by John Calhoun. He writes:

I have a friend who's a mostly out-of-work house painter. One day he stopped at a red light with his truck, you know with the ladders on top and all that jazz, and he hears a toot from the vehicle stopped next to him. The fellow motions to him to roll down his window and then asks the painter if he's looking for work.

'You bet I am!'

'Do you have a business card?' asks the prospective customer.

He fumbles around for one like everyone does who doesn't have a business card and finally admits, 'No I don't have one.' And the painter says, 'Tell me your number. I'll remember it and I'll give you a call tomorrow.'

The fellow in the other vehicle starts to rattle off the number.

Same area code as me, the painter thinks, 'I won't have any trouble remembering that.' Next comes the three-digit exchange. 'Ha! Same as mine. All I have to remember then is the last four digits. Piece of cake.'

The light turns green and even though their accelerating engines are making a lot of noise, they can't drown out those last four digits. He's got them. And upon hearing them, he thinks, 'Boy, this is my lucky day.' One of those digits is his son's age, the next one his daughter's age. A third one is the number of months he's behind on his boat payments. And the fourth one is the number of nights his wife has made him sleep on the sofa. He's a snorer, I guess.

Now he realizes that the four-digit number is divisible by three. He says, 'Great! I'll remember the number and I'll call this guy first thing in the morning.'

Well, three days later he realizes that he forgot to make the phone call. So he sits down with a paper and a pencil so he can write down the number. He knows the area code, it's the same as his, right? He knows the next three digits, they're the same as his. 'Now those last four digits, let me see,' he says. 'One of them is the number of nights I have spent on the sofa, that's easy. Oh yeah, and there's my boat payment default status. I got that. My daughter's age, and my son's age.' And then he remembers that the four-digit number he just reconstructed is divisible by three. He does it, he divides it by three and says, 'Eureka! Yeah, I got the number.'

He makes the call. It's the wrong number. It's a retired proctologist, who told him what to do with his paintbrush. Anyway, something went terribly wrong. What was it, and why?
RAY: Here's the answer. If you paid attention, the painter obviously got the order wrong.

TOM: Oh.

RAY: He did have a four-digit number that was divisible by three, but it turns out that if you have a four-digit number or a five-digit number, any digit number, if it's divisible by three no matter how you rearrange the digits, that other number is also divisible by three. And it turns out with a four-digit number, there are 24 ways to arrange those digits.

So he dialed one number. There are 23 others. So he might dial 22 more before he finally gets the correct number. So who's our winner?

TOM: Our winner this week is Larry Klein from Phoenix, Arizona. And for having his answer selected at random from among all the correct answers that we got, Larry's going to get a $26 gift certificate to the Shameless Commerce Division at With which Larry can pick up a four-pack of Car Talk reusable shopping bags.

RAY: Congratulations, Larry!

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