RAY: Hi, we're back. You're listening to Car Talk with us, Click and Clack, the Tappet Brothers, and we're here to talk about cars, car repair and the answer to last week's Puzzler. And I neglected to mention who sent this in last week.
TOM: Oh, oh. You're covering your tracks so early?
RAY: No, no, no. Oh, no, no. This is right on the, this is right on the, this is Max, sent in by Max Chamberlain. I don't know where he's from. Some place out in the Internet world.
TOM: Not Lord Chamberlain, is it?
RAY: No, but --
TOM: I went to high school with a guy named Lord Chamberlain.
RAY: You did? Really? Anyway, here it is, and I thought it was pretty cute and that's why I used it. Imagine you have in front of you two cardboard cubes and a Magic Marker and what you'd like to do is use the cubes to represent the date. For example, if today were the third of the month, one cube would have a zero and the other one a three. If it were the 12th, one cube would have a one and the other a two. You got it?
TOM: I got it.
RAY: So your job here --
TOM: Mmm-hmm.
RAY: -- is to write on the cubes. OK? Now, each cube has six sides, so you have 12 faces altogether. OK?
TOM: Yeah.
RAY: I guess it's a two-part question. Is it possible to represent every day of the month from the first to the 31st using just these two cubes, and how is it possible?
TOM: Yeah.
RAY: And I think I gave the hint, think outside the box.
TOM: I got it. I've got my, I'm drawing my two cubes here right now.
RAY: You don't need to draw them as cubes. You need to rather draw them as just squares.
TOM: As six faces.
RAY: OK? You've got 12 faces altogether.
TOM: I've got 12 faces altogether.
RAY: So we agree that one cube has to have a zero, a one and a two and another cube, the other cube has to have a zero, a one and a two.
TOM: Yes, it does.
RAY: And one of the cubes has to have a three.
TOM: One of them has to have a three, but the other one does not.
RAY: Does not. OK? Because there's no 33rd of the month.
TOM: So we're going to put the three on Cube Number One.
RAY: OK? So, Cube Number One has zero, one, two, three, and Cube Number Two has zero, one, two. Now here's the problem. That is how many faces altogether? That's seven faces used up.
TOM: Seven faces.
RAY: And then we have to put a four, a five, a six, a seven, an eight and a nine, and that's six more faces. We only have five faces left.
TOM: One, two, three, four, five, six, seven. We only have five left, and we need six.
RAY: We need six. Can it be done?
TOM: Yes.
RAY: Well, yes, it can be done.
TOM: Yes, it can.
RAY: Because you don't need both a six and a nine --
TOM: ŚCause cubes work both ways --
RAY: Because you --
TOM: Upside down.
RAY: You flip the six and it becomes a nine and vice versa, and so you can eliminate one of those and you --
TOM: Where you going to put them though?
RAY: Well --
TOM: Does it matter?
RAY: Doesn't matter. You put --
TOM: Well, sure it matters.
RAY: It does matter.
TOM: Sure it matters.
RAY: Yeah, but the, that's the easy part. The hard part was figuring out that you could use a six for a nine and vice versa, that you could in fact get all the numbers you needed on 12 faces and not worry about having both the six and the nine.
TOM: Sure.
RAY: Right? Do we have a winner?
TOM: And you're doing the high numbers on the one that doesn't have the three. Right?
RAY: Right.
TOM: 'Cause there are no 36ths of the month.
RAY: Right. Right.
TOM: OK, and now I get it.
RAY: Yeah. So --
TOM: OK.
RAY: ŚCause in fact, one of them is going to have zero, one, two, three, four and a five. And the other has zero, one, two, six, seven and eight.
TOM: Ah. How sweet it is.
RAY: OK? You happy?
TOM: And the winner. Yes, we have a winner. The winner is Derward Thompson from Corpus Christi, Texas. And for having his answer selected at random from both of the answers that we got, Derward is going to get a $25 gift certificate to the Shameless Commerce Division which is at the Car Talk section of cars.com. And with that gift certificate, he can be the first person in the great state of Texas to get a copy of our brand-new CD, "The Hatchback of Notre Dame, More Car Talk Classics." What a lucky guy.
[ Car Talk Puzzler ]
