# A Calendar Puzzle

A simple little puzzle. Suppose you are given two ordinary 6 sided dice. Is it possible to put the numbers 0-9 (with repetition) onto the faces of both dice, such that using both dice you can display all the days of the month i.e. 01 – 31 .

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### 10 Responses to A Calendar Puzzle

1. pAt84 says:

No, impossible but you can imagine a dice with seven faces. :p

If you have too much time, you can give the following a try:
problem

which was simplified from the
original

By the way: I didn’t read all of your blog, what was your first paper about?
Merry christmas,
Pat

2. pAt84 says:

oops, I am sorry. Should have used html-tags.

3. splineguy says:

Can’t be done.

My reasoning is as follows. Each of the dice must have a 1 and 2, in order to denote 11 and 22. This leave 4 spaces on each die, which in order to denote 01 – 09, we must put a 0 on each of the dice. This leaves 3 space on each die, which if we only but the remaining numbers 4 – 9 (7 total), will not fit in the remaining six places.

Is there a more elegant proof?

4. tpc says:

pAt84,

I have modified your post and also posted your problem, hope you do not mind. I believe there is a typo?

My paper is about powers of Dedekind eta function.

5. tpc says:

splineguy,

It can be done. The puzzle came from a real life desktop calendar. I’ll try and buy one and post photos.

Your answer is epsilon close. Since it is a cube, you can flip the 6 over to get a 9.

6. splineguy says:

Nice, very nice. I don’t know why, but I was visualizing dots on the dice.

7. Bruce says:

Just a guess… get rid of the extra zero… day one doesn’t need to read 01, just 1.

8. Anonymous says:

1st die: 0 1 2 4 5 9
2nd die: 0 1 2 3 7 8

9 6

9. One die is going to be the tens column, one is going to be the ones.
You need a zero, one and two on each die to account for the tens column in your rolls.

One die will have a 3, 4, and 5; the other will have a 6, 7, and 8. The 6 can be reversed to act as a 9.

so, first die: 0 1 2 3 4 5
second die: 0 1 2 6 7 8

From this combination you can get every number from 01 to 31. You can also get spurious numbers like 00, 58, 71, etc. The rules don’t say you can’t do that, though.