Calendar made of dice

Problem

You are a crazy guy who dislike traditional calendar. Rather, you use 2 dice to help you organize the date instead. With 2 dice, you want to present the day of the month. And for each die, you assign a single number digit from 0-9. Note that for day of the month less than 10, you have to use the first digit of 0 to represent it (for e.g, day 5 must be represented as 0 5). And you can swap the order of the dice to represent the day. So, for each die, what set of digits do you assign?

---

Hints

Hint 1

In both dice, there must be certain same digit identities.

Hint 2

1,2, and 0 must definitely be present in each die.

Hint 3

That leaves each die with 3 slots left. However, there are still 7 candidates left to assign.

Hint 4

Pay attention to the digit 6. It can be flipped to represent 9.

---

Solution

Show Solution

Die 1: 0,1,2,3,4,5
Die 2: 0,1,2,6,7,8

Show Explanation

As there are days: 11 and 22, 1 and 2 must be present in both dice. In addition, to cover all single-digit days, 0 must be present in both dice. And use the fact that a 6 can be flipped to make a 9, we assign the rest of the candidates to each die to form the final result:

Die 1: 0,1,2,3,4,5
Die 2: 0,1,2,6,7,8