Two little cubes - and too many numbers.

Jun 13, 2005

RAY: I didn't have to obfuscate this puzzler a whole lot, but I did make a few little changes. This came from Jonathan Cox, from across the pond. He writes:

I'm getting old and a little absent-minded, so my friends got together and bought me a stylish little desk calendar. It's a cradle for two cubes, each with one number per face.

They figured I probably had enough left in me to figure what year it was and what month it was, but the date was going to elude me. So, this little gift was going to show the date. So, for example, if it were the 21st, I'd rotate one cube until a "2" was showing, and the other would show a "1." The next day I would know to rotate one cube so, together, the two cubes would read "22."

With the two cubes, I was able to express every date. For example, if it were the 2nd of the month, it would be expressed as "02." If it were the 18th you'd put up a 1 and an 8, and so on.

Here's my question. If you were designing the cubes, what numbers would you paint on each one so you could express all the dates from "01" to "31"?

Here're a few hints: you're going to run into a problem because you're not going to have enough faces. Maybe. There are several right answers and lots of wrong answers. But all the right answers have one thing in common.
RAY: Well, you have two cubes with six faces each, so that's 12 faces. Let's see what we need. Each cube needs a one, right? Because you have to be able to express the 11th.

TOM: And two twos.

RAY: Right. You need one three, right? After all, there's no 33rd of the month. But each cube also needs a zero.

Let's look what we got so far. We've got one cube at zero, one, two, three. That's four faces. And another cube has zero, one, two. So I've used seven faces, I've got five left. So I need to have a four and a five, a six, a seven, an eight and a nine.

Oops - that's 13 faces, and we only have 12 to use.

TOM: You've got to turn the six upside down.

RAY: Exactly. So, for example, one cube could say, zero, one, two, four, seven, eight, and the other could say zero, one, two, three, five, nine or six.

The six and the nine are redundant. Cute, huh?

Do we have a winner?

TOM: Of course! The winner is James Dawson from Crane, Texas. And for having his answer selected at random from among all the correct answers that we got James gets a 26-dollar gift certificate to the Shameless Commerce Division at with which James can get a combination Car Talk baseball jersey/dipstick wiper. Super absorbent cotton makes it perfect for both applications, we think, and we know which one it's more likely to be used for.

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