Seven Flipped Poster

In this problem it doesn't matter where you start on the picture. 
1) Pick any 3 hexagons (they will turn blue)
2) Pick 2 more hexagons and then pick one that you chose in the first go. You should now have 4 hexagons blue.
3) Finally pick the three remaining red hexagons.

So, it will take three moves.

If the number of tiles is a multiple of 3, the number of moves is the number of tiles divided by 3.

If the number of tiles is one more than a multiple of 3, you add 1 to the number of moves for the number of tiles immediately below it. For example, for 6 tiles it is 3 moves, for 7 tiles it is 4 moves

If the number of tiles is two more than a multiple of 3, you add 2 to the number of moves for the number of tiles immediately below it. For example, for 6 tiles it is 3 moves, for 8 tiles it is 5 moves