0: 6 segments lit: abcefg
  aaaa
 b    c
 b    c
  ....
 e    f
 e    f
  gggg

1: 2 segments lit: cf
  ....
 .    c
 .    c
  ....
 .    f
 .    f
  ....

2: 5 segments lit: acdeg
  aaaa
 .    c
 .    c
  dddd
 e    .
 e    .
  gggg

3: 5 segments lit: acdfg -> 7+dg
  aaaa
 .    c
 .    c
  dddd
 .    f
 .    f
  gggg

4: 4 segments lit: bcdf -> 1+bd
  ....
 b    c
 b    c
  dddd
 .    f
 .    f
  ....

5: 5 segments lit: abdfg
  aaaa
 b    .
 b    .
  dddd
 .    f
 .    f
  gggg

6: 6 segments lit: abdefg
  aaaa
 b    .
 b    .
  dddd
 e    f
 e    f
  gggg

7: 3 segments lit: acf -> 1+a <-- this means we can work out a
  aaaa
 .    c
 .    c
  ....
 .    f
 .    f
  ....

8: 7 segments lit: abcdefg
  aaaa
 b    c
 b    c
  dddd
 e    f
 e    f
  gggg

9: 6 segments lit: abcdfg
  aaaa
 b    c
 b    c
  dddd
 .    f
 .    f
  gggg

0: abc efg -> 1 + 2 + 4 + 16 + 32 + 64       -> 119
1:   c  f  -> 4 + 32                         -> 36
2: a cde g -> 1 + 4 + 8 + 16 + 64            -> 93
3: a cd fg -> 1 + 4 + 8 + 32 + 64            -> 109
4:  bcd f  -> 2 + 4 + 8 + 32                 -> 46
5: ab d fg -> 1 + 2 + 8 + 32 + 64            -> 107
6: ab defg -> 1 + 2 + 8 + 16 + 32 + 64       -> 123
7: a c  f  -> 1 + 4 + 32                     -> 37
8: abcdefg -> 1 + 2 + 4 + 8 + 16 + 32 + 64   -> 127
9: abcd fg -> 1 + 2 + 4 + 8 + 32 + 64        -> 111

a: 8
b: 6
c: 8
d: 7 - only one that's exactly a 7 count
e: 4 - only one that's exactly a 4 count
f: 9 - only one that's exactly a 9 count
g: 7