Brain Teasers | Calendar Cube

 Question: 

 

Cookie has two custom-made dice(Dice A and Dice B). Instead of numbers 1 - 6, she can place single-digit numbers on the faces of each dice so that every morning she can arrange the dice in a way as to make the two front faces show the current day of the month. She must use both dice i.e. days 1 — 9 must be shown as (01 — 09), but she can switch the order of the dice if she wants.  

What numbers should she put on the six faces of each of the two die to achieve the same? 

 

 

Solution: 

 

We will start by finding 2 digit numbers that will appear on both dice. 

As 11 and 22 are two possible dates, hence 1 and 2 should appear on both dice. 

 

Now to express single-digit numbers we need 0 on one of the dice. For example – 08  

Since we need to express all the digits as single-digit numbers so having 0 on one of the dice will not be enough as the other dice will not have every single-digit number. Hence we need to have 0 also on both the dice. 

 

Current State: 

Dice A  

1 

2 

0

  

  

  

Dice B 

1 

2 

 

 

 

 

 

Now we need to arrange 3,4,5,6,7,8,9 

 

We have seven unique numbers but only six spaces. If we observe closely 6 can be used as 9 and vice versaNow we are left with six unique numbers - 3,4,5,6,7,8 

 

We can simply arrange 3, 4, 5 on Dice A and  6, 7, 8 on Dice B 

 

Final State: 

Dice A 

1 

2 

0

3 

4 

5 

Dice B 

1 

2 

0

6 

7 

8 


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