| steps (in any order) | number of steps | Permutations | |
all ones | 1,1,1,1,1,1,1,1,1 | 9 | 1 | 1 |
ones and 2s | 1,1,1,1,1,1,1,2 | 8 | 8 | 8 |
1,1,1,1,1,2,2 | 7 | 7C2 | 21 | |
1,1,1,2,2,2 | 6 | 6C3 | 20 | |
1,2,2,2,2 | 5 | 5 | 5 | |
ones and threes | 1,1,1,1,1,1,3 | 7 | 7 | 7 |
1,1,1,3,3 | 5 | 5C2 | 10 | |
all threes | 3,3,3 | 3 | 1 | 1 |
twos and threes | 2,2,2,3 | 4 | 4 | 4 |
ones, twos and threes | 3,2,1,1,2 | 5 | 5*4C2 | 30 |
3,2,1,3 | 4 | 4*3 | 12 | |
3,2,1,1,1,1 | 6 | 6*5 | 30 | |
TOTAL | 149 |