The two dice calendar problem

I bought this calendar in Marrakesh last month. You show the date by aligning the two special dices the right way, and the month by aligning one of three small wooden bricks at the bottom. Four sides times three bricks equal twelve months. But the interesting thing is the two dices.

The question is, how would you place numbers on them to be able to show all the dates from 01 to 31 ?

One of my most popular articles ever is a complicated mathematical experiment, so maybe there are someone out there that find this small challenge interesting.

The usual layout for a dice would be like this:

Or simply like this:
-3-
265
-4-
-1-

But if you try to use two dices like that to show dates between 1 and 31 you would get some trouble at once. The lowest number you can show is 11. You need 0. And you don’t have 7,8 and 9…

So my question is: could you describe the layout on the two dices in my calendar from Marrakesh? You can answer through a comment here or a trackback to your own blog. Simply use the same kind of number layout that I used above to show a standard dice.

I’ll get back here with the answer. I don’t operate with deadlines on eirikso.com, but how about this? The sixth article from now will be the answer. I usually post two or three articles each week, so expect the answer in two or three weeks. Or, as soon as someone post a comment with the right layout.

The two dice calendar problem

10 thoughts on “The two dice calendar problem

  1. CurryPower says:

    Wow, quite a way to start a Sunday morning. I had to twist my head for a few minutes, but with som help from a friend I managed to solve it. It’s quite simple really.

    The numbers 0, 1 and 2 have to be on both dice, the remaining numbers from 3 to 9 you can spread on the two dice. But, you might say, it’s not more than six sides left on the two dice to place seven numbers on. Well the solution to that is to let the 6 also be a 9. Since we are not gonna throw the dice, the layout is not really important, but I can do it anyway.

    Die no. 1:
    -0-
    126
    -7-
    -8-

    Die no. 2:
    -0-
    123
    -4-
    -5-

  2. “I’ll post the answer in a couple of weeks”. Yeah, right. Or my readers will solve this in a couple of hours. And it doesn’t matter if this article was posted early Sunday morning.

    Two answers already and both of them are right. Yes, the 6 doubling as a 9 was the small extra problem. And the reason for the fact that it is possible to build a calendar like this.

    Oyvind S:
    I published your excel sheet here:
    http://spreadsheets.google.com/pub?key=pqnGZVmnZ3SKQBt8425uBVQ

  3. Trond says:

    Hmm, They have different sizes. I guess the solution doesnt demand that the small one should be to the left, and the large one to the right?

  4. As far as I remember I bought it in a big so called “fixed price” shop. Probably something for tourists, but very easy to handle for us non-bargaining people from the north. :-)

  5. vishtu says:

    ok your problem is that you need a 0 on both a 1 on both and a 2 on both but the solution is easy 6 and 9 are interchangible so
    -0-
    123
    -4-
    -5-

    -0-
    126
    -7-
    -8-

    and there you go

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