Sum of Scores of 2 Dice

2 3 4 5 6 73 4 5 6 7 84 5 6 7 8 95 6 7 8 9 106 7 8 9 10 117 8 9 10 11 12

1 2 3 4 5 6123456

How would you represent the sum of scores on 2 dice?

How would you represent the sum of scores on 3 dice?

2 3 4 5 6 73 4 5 6 7 84 5 6 7 8 95 6 7 8 9 106 7 8 9 10 117 8 9 10 11 12

1 2 3 4 5 6123456

Take all the possible sums of 2 dice and then imagine you get a one on the next dice.

What would all the possible sums be for this scenario?

3 4 5 6 7 84 5 6 7 8 95 6 7 8 9 106 7 8 9 10 117 8 9 10 11 128 9 10 11 12 13

9 10 11 12 13 14

4 5 6 7 8 95 6 7 8 9 106 7 8 9 10 117 8 9 10 11 128 9 10 11 12 13

Take all the possible sums of 2 dice and then imagine you get a two on the next dice.

3 4 5 6 7 84 5 6 7 8 95 6 7 8 9 106 7 8 9 10 117 8 9 10 11 128 9 10 11 12 13

A reminder of the sum of three dice with the last number being one.

Do we have to do this another four times or can anyone see a quicker way by looking at these two examples?

Score Number of Occurences

3 1

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

3

6

10

15

21

25

27

27

25

21

15

10

6

3

1

1) What is the probability of scoring 10 when you roll 3 dice? (Decimal)

2) What´s the probability of scoring 18 when you roll three dice? (Decimal)

3) Why is the distribution symmetrical?

4) Can you see any special number sequences in the table?

5) Why does this sequence only exist up to a score of 8?

28 ???

3 4 5 7 8 64 5 7 8 9 65 7 8 9 10 6 7 8 9 10 11 7 8 9 10 11 12 8 9 10 11 12 13

6

First Layer

4 5 7 8 9 65 7 8 9 10 6 7 8 9 10 11 67 8 9 10 11 12 8 9 10 11 12 13

Second Layer

9 10 11 12 13 14

5 7 8 9 10 6 7 8 9 10 11 67 8 9 10 11 12 8 9 10 11 12 13

Third Layer

9 10 11 12 13 14 10 11 12 13 14 15

7 8 9 10 11 67 8 9 10 11 12 8 9 10 11 12 13

Third Layer

9 10 11 12 13 14 10 11 12 13 14 15 11 12 13 14 15 16

4 + 3 + 2 + 1= 10 different ways to get a 6

Why doesn´t a score of 9 fit the sequence?

We just figured out that the score of 10 should occur just as frequently as a score of 11. Why hasn´t this happened?