Problem Teachers' Notes Hint Solution

Fair Exchange

8 - 6 ways:

5, 2, 1
5, 1, 1, 1
2, 2, 1, 2, 1 = 2, 2, 2, 1, 1
2, 2, 1, 1, 1, 1
2, 1, 1, 1, 2, 1 (same as above)
2, 1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1, 2, 1 (same as above)
1, 1, 1, 1, 1, 1, 1, 1

11 - 9 ways:

5, 5, 1
2, 2, 1, 5, 1 = 5, 2, 2, 1, 1
2, 1, 1, 1, 5, 1 = 5, 2, 1, 1, 1, 1
1, 1, 1, 1, 1, 5, 1 = 5, 1, 1, 1, 1, 1, 1
2, 2, 1, 2, 2, 1, 1 = 2, 2, 2, 2, 1, 1, 1
2, 2, 1, 2, 1, 1, 1, 1 = 2, 2, 2, 1, 1, 1, 1, 1
2, 2, 1, 1, 1, 1, 1, 1, 1
2, 1, 1, 1, 2, 1, 1, 1, 1 (same as above)
2, 1, 1, 1, 1, 1, 1, 1, 1, 1
1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1