Car Talk Weekly Puzzler 08-02-16
Received this puzzle via email today. How do you make a 31 day calendar (each day being double digits) using 2 cubes, with each face only having a single digit?
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.
My solution is below. Double 0, 1, and 2. Leave out the 9 and the 6 will pull double duty, it will represent every 6 and 9. Simply flip it whichever way it’s needed. To be perfectly honest, I already knew it was very much possible. When I was little my mom actually had one of these calendars, and it even had another set of rectangular prisms, with each face having the name of a month. They’re called perpetual calendars. It requires manual operation, but it’s good for every day of every year.
And here’s what an actual perpetual calendar looks like: Wood Block Perpetual Calendar by TheDutchHospital on Etsy
I liked that shot because it shows how it works, including the month blocks. They make pretty nice desk calendars