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Help with this hard counting problem

 

When two standard 6-sided dice are rolled, there are 36 possible outcomes for the sum of the two rolls: one sum of 2, two sums of 3, and so on, up to one sum of 12.

 

Find all possible ways of numbering two 6-sided dice with positive integers (not necessarily distinct), so that when they are rolled, the 36 possible outcomes for the sum of the two rolls are the same as the 36 possible outcomes for the sum of two standard 6-sided dice.

 Apr 19, 2023
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Why is it "hard counting question" ?

 

When you roll 2 dice, how would you get the sum of 2? Well, you can only get the sum of 2 if you roll 2 "ones". Because: 1 + 1=2. Right? How would you get the sum of 3? Again, you can only get the sum of 3 if you roll one "1" and one "2". Because: 1 + 2=3 and 2 +1 =3.......and so on.

 

Go through all the numbers from 2 to 12, because 12 is a maximum you can get from rolling 2 dice, and that can only happen if you roll 2 "sixes", because: 6 + 6=12

 Apr 19, 2023

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