Seven Flipped

You have seven hexagonal-shaped mats in a line.
These mats all have to be turned over, but you can only turn over exactly three at a time.
You can choose the three from anywhere in the line.
A mat may be turned over on one move and turned back over again on another.

What is the smallest number of moves you can do this in?
Try with other numbers of mats.
Do you notice any patterns in your findings?
Can you explain why these patterns occur?

You might like to use the interactivity to have a go. Click on the three hexagons which you would like to turn over. The mats are red on one side (this side is face up to start with) and purple on the other.

Full Screen Version

A poster of this problem is available here.