Painting by Numbers

The Puzzler

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!

[ Car Talk Puzzler ]

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