Problem Teachers' Notes Hint Solution

# Playing Connect Three

Interactivity
There are 36 possible dice combinations:
1 & -1
1 & -2
1 & -3
etc., etc...
Each combination allows for 3 different totals:
A + B
A - B
B - A
So there are 108 different arrangements to be considered.
Number of ways of achieving each total:

possible totals | number of ways
12 | 1
11 | 2
10 | 3
9 | 3
8 | 3
7 | 3
6 | 3
5 | 5
4 | 7
3 | 8
2 | 7
1 | 6
0 | 6
-1 | 6
-2 | 7
-3 | 8
-4 | 7
-5 | 5
-6 | 3
-7 | 3
-8 | 3
-9 | 3
-10 | 3
-11 | 2
-12 | 1