# Two dice make a calendar

Little riddle: if you have two dice (so each has 6 sides), with 1 digit on each side and you want to be able to form all numbers between 1 and 31 (for the days of the month), what digits would be on each dice? E.g. if dice #1 has 0-1-2-3-4-5 and the second 4-5-6-7-8-9, it won’t work, because you cannot form the number ’22’.

Try to guess and I’ll give the answer next week. There’s a little trick involved! I first tried to figure it out without looking at the dice, and I enjoyed the mind gymnastics.

### 23 thoughts on “Two dice make a calendar”

1. Pascal

(for the non-Dutch speakers… I meant: “done it without looking at dice and without writing anything down”)

2. Clopin

Hmm, one question though: is it allowed to leave dice out from time to time? Because I could have a problem in the first 10 days 😉

3. Inferis

@Clopin: I struggled with that too, but the riddle says “1 to 31”, so I assumed it was okay to represent the first 9 days using 1 dice.

4. Pascal

@Clopin and @Inferis:

No, you need to have two dice, otherwise it wouldn’t be much fun…
So: you need to have “0” on one or both dices.
Oh, and may I point out that the digits are Arabic, and not represented by numbers of dots?

5. Stijn

*spoiler warning*

I think I got it right. (:

Dice A: zero-one-two-three-seven-eight
Dice B: zero-one-two-four-five-six

The six can be used as a nine as well.

6. Brian

With the 123456 and 789120 solution, the 1 in either die can be used as a “dash” so that two die could still be used to represent the first 9 days. That is: -1, -2, -3, etc.

7. Srinu

Dice 1 : 0 1 2 3 4 5
Dice 2 : 0 1 2 6 7 8

This is exact solution for this question..