Date Dice Dilemma

Question

My cousin just learned about numbers and dates in school and I would like to give him a little present: A set of (regular, six-sided) dice with which he can display the current date if he turns them the right way.

When he places the dice, they should be able to display the date of every day and month of the year in the following format:

[M][M] [D][D]

So, if it's the third of September, I want him to be able to place the dice in a way that they show:

[0][9] [0][3]

Now my question:

What is the minimum amount of dice I need to make, and what numbers should I put on each die?

I am going to be honest: He is a great kid, but if this turns out to be too much work - he will get coals for Christmas.

Answer 1

My answer:

4 dice. (6 faced).

Numbers on each die:

2 sets of the following 2 dice.
0, 1, 2, 3, 4, 6
0, 1, 2, 5, 7, 8

Reasoning:

1 set will be used for the month and one set for the day.
I will explain how you can get all the numbers from 1 to 31 using one set of dice described above. If you can do it for the day (up to 31) you can do it for the month also with the other set (up to 12).
Let's name the dice A and B in the order listed above.

.

01 - A0, B1
02 - A0, B2
03 - A0, B3
04 - B0, A4
05 - A0, B5
06 - B0, A6
07 - A0, B7
08 - A0, B8
09 - B0, A6 reversed
10 - A1, B0
11 - A1, B1
12 - A1, B2
13 - A1, B3
14 - B1, A4
15 - A1, B5
16 - B1, A6
17 - A1, B7
18 - A1, B8
19 - B1, A6 reversed
20 - A2, B0
21 - A2, B1
22 - A2, B2
23 - A2, B3
24 - B2, A4
25 - A2, B5
26 - B2, A6
27 - A2, B7
28 - A2, B8
29 - B2, A6 reversed
30 - A3, B0
31 - A3, B1

Additional reasoning:

Because you have the numbers 11 and 22 it means 1 and 2 need to go on every die.
You need one die to have a 0, but you cannot form 9 numbers (1 to 9) from a single die, so you need 0 on both of them.
Summarize: We now have 2 dice with the number 0,1 & 2.
Since we need all the digits we need somehow to add the remaining 7 digits in the remaining 6 available faces.
Since 6 can double as a 9 and we never have to create the numbers 66, 69,96 or 99 we get to have 6 number on 6 faces. Just split them 3 on one die and 3 on the other. I don't think the order is important.

Answer 2

The answer is

4

if you note:

You never specified what type of dice. I could use 10 sided dice in this instance with the digits 0-9 on them. And, if you allow more than one digit per dice (unclear), we could go lower.

Answer 3

It will not be the answer as it doesn't follow the formatting but you can use only 3 dices.

You only use one type of dice: 0 I II III following each other and X and V on opposite sides.

The trick is, for the month, you show two faces at the same time. Thus you can get the following combination IV VI VII VIII IX.

Same reasoning for the second numeral of the day.