The Cube Calendar Conundrum

Feb 06, 2016

RAY: This came from Jonathan Cox, from across the pond. He writes:

I have a stylish little desk calendar that consists of a cradle for two cubes, each with one number per face. Together, the two cubes show what day of the month it is. 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 can express every date. For example, if it were the 2nd of the month, it would be expressed as "02." If it were the 18th I'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. Each cube needs a one, right? Because you have to be able to express the 11th. You also need two twos. But you only need one three, because there’s no 33rd of the month.

Each cube also needs a zero. So let's look what we’ve 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.

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.

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