## Puzzle 6: Flipping Cards

There are 7 cards sitting face down on table top. You want to turn them all face up in the smallest number of moves. A "move" consists of turning over 3 cards at a time. The cards don't have to be adjacent, but you must turn over three at a time. How many moves are required?

Extension: What about adding 2 cards and flipping one extra card each move? How many moves would it take to have all cards face up? For example, if there are 9 cards, flip 4 at a time, how many moves would make all the cards facing up? Can you see the pattern and prove it?

Extension: What about adding 2 cards and flipping one extra card each move? How many moves would it take to have all cards face up? For example, if there are 9 cards, flip 4 at a time, how many moves would make all the cards facing up? Can you see the pattern and prove it?