Three dice

Date: Mon, 16 Nov 1998 19:32:26 -0800
Subject: Math problem

Rolling three regular dice how many different ways could a sum of 10 be rolled?

Hope you can help. Can you please show me how this is done?

Signed : Ryan/ age 12

Hi Ryan
I think that one is best to think of a Red,a Green and a Blue dice. The ways to get a sum of 10 from three of the numbers 1, 2, 3, 4, 5, 6 are, first of all:

6 + 3 + 1
6 + 2 + 2
5 + 4 + 1
5 + 3 + 2
4 + 4 + 2
3 + 3 + 4.

But how many ways can this happen? There are many more than 5 ways, in fact there are 27 as follows -- where we have to take into account the colour of each number thrown:

6 + 3 + 1	R	G	B
	6	3	1
	6	1	3
	3	6	1
	3	1	6
	1	6	3
	1	3	6

5 + 4 + 1	R	G	B
	5	4	1
	5	1	4
	4	5	1
	4	1	5
	1	5	4
	1	4	5

5 + 3 + 2	R	G	B
	5	3	2
	5	2	3
	3	5	2
	3	2	5
	2	5	3
	2	3	5

4 + 4 + 2	R	G	B
	4	4	2
	4	2	4
	2	4	4

6 + 2 + 2	R	G	B
	6	2	2
	2	6	2
	2	2	6

3 + 3 + 4	R	G	B
	3	3	4
	3	4	3
	4	3	3

Cheers
Penny

Go to Math Central

To return to the previous page use your browser's back button.