Puzzler

This week’s Car Talk Puzzler is a great one:

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”?

Easy, right?

Yeah, sure. Now that you’ve figured that one out, genius, try this one on for size, of my own device:

How many unique solutions are there to the above puzzle?

Consider an individual cube “unique” if there is no way it can be rotated to match another cube. To make an analogy with gambling dice, giving the faces in the order (front, right, back, left, top, bottom):

1, 2, 6, 5, 4, 3

is identical to

1, 4, 6, 3, 2, 5

since the latter can be derived from the former by rotating the former 90 degrees to the right around the z-axis.

Good luck.

posted by Chris on 14 June 2005 at 0009 in entertainment

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