# Working in a hypercube with faces
# Top:    Bottom:  Side:
# 1 - 7   6 - 4    1 - 8
# |   |   |   |    |   |
# 8 - 2   3 - 5    6 - 3
# (absolute difference across diagonals is always 4)
# Thinking of vertices 1,2,3,4 as red and 5,6,7,8 as blue 
# Want all paths of length 5 with 3 red vertices
# Grouped in such a way that the first vertex is the red degree-2 vertex,
# the next are its neighbors, and the final two are the leaves
# The solution should be 5/108 so we multiply by 108 to see it 
108 5 0  1 7 8 3 4  
108 5 0  1 6 7 2 3  
108 5 0  1 6 8 2 4  
108 5 0  2 5 7 1 3  
108 5 0  2 5 8 1 4  
108 5 0  2 7 8 3 4  
108 5 0  3 5 6 1 2  
108 5 0  3 5 8 1 4  
108 5 0  3 6 8 2 4  
108 5 0  4 5 6 1 2  
108 5 0  4 5 7 1 3  
108 5 0  4 6 7 2 3  
# 4 should be our empty one
0
0
30 1 0 1 
-30 1 0 4
0
0
30 1 0 2 
-30 1 0 4
0
0
30 1 0 3 
-30 1 0 4
0
0
30 1 0 1
30 1 0 2
30 1 0 3
30 1 0 4
-30 1 0 5
-30 1 0 6
-30 1 0 7
-30 1 0 8
0
0
-30 1 0 1
-30 1 0 2
-30 1 0 3
-30 1 0 4
30 1 0 5
30 1 0 6
30 1 0 7
30 1 0 8
