Seven Flipped
Each hexagon must be flipped over an odd number of times.
For seven hexagons - three moves. If hexagons are numbered from 1
to 7 starting at the left, then moves are, for example:
1. Flip 1, 2, 3
2. Flip 3, 4, 5
3. Flip 3, 6, 7
For three hexagons - one move (easy!).
For four hexagons - four moves. If hexagons numbered as above,
then:
1. Flip 1, 2, 3
2. Flip 1, 2, 4
3. Flip 1, 3, 4
4. Flip 2, 3, 4
For five hexagons - three moves:
1. Flip 1, 2, 3
2. Flip 1, 2, 4
3. Flip 1, 2, 5.
For six hexagons - two moves:
1. Flip 1, 2, 3
2. Flip 4, 5, 6.
For eight hexagons - four moves: turn three in one
move, then left with five hexagons which is three moves.
For nine - three moves.
For ten - one more than seven moves, so four.
Generally:
If no. hexagons a multiple of 3, then smallest number of moves is
number of hexagons divided by 3.