Days of month using 2 dice | Puzzles for Interview - Interview Preparation PDF Download

Problem Statement

The challenge is to find a way to represent all the days of the month, ranging from 1 to 31, using two 6-sided dice. Each dice face can have a number written on it, from 0 to 9. For example, to represent the number 1, one dice should show 0 and the other should show 1. Similarly, to represent the number 29, one dice should show 2 and the other should show 9.

Solution

To solve this problem, we need to ensure that each dice has an appropriate set of numbers on its faces such that all combinations from 1 to 31 can be represented. We can assign the numbers on the two dice as follows:

Dice 1: 0, 1, 2, 3, 4, 5

Dice 2: 0, 1, 2, 6, 7, 8

By assigning these numbers to the dice, we can represent all the days of the month using the following combinations:

• For days 1 to 6, roll a 0 on Dice 1 and the corresponding number on Dice 2 (1-6; note that the 6 on Dice 2 represents a 9).
• For days 7 to 12, roll a 1 on Dice 1 and the corresponding number on Dice 2 (0-5).
• For days 13 to 18, roll a 2 on Dice 1 and the corresponding number on Dice 2 (0-5).
• For days 19 to 24, roll a 3 on Dice 1 and the corresponding number on Dice 2 (0-5).
• For days 25 to 30, roll a 4 on Dice 1 and the corresponding number on Dice 2 (0-5).
• For day 31, roll a 5 on Dice 1 and 0 on Dice 2.

Notice that by swapping the 9 on Dice 2 with a 6, we can still represent the number 9 by flipping the dice upside down.

Conclusion

By carefully assigning the numbers on the faces of the two 6-sided dice as shown above, it is possible to represent all the days of the month, ranging from 1 to 31. This solution makes use of the flexibility of the dice and the ability to flip the dice upside down to represent different numbers.