To further elaborate on what vee41 was saying.
Basically you would create one sprite representing the game board.
You could vary up the look of the piece, by using a different frame of animation for a different "look" to the piece if it has a variety of types lets say.
Then you would give it one variable called "visited"
When you create multiple instances of the board square, each one will then have its own "visited" variable that will keep track of itself
then you would simply code something like this.
player is overlapping object "board piece"
-> set "visited" to 1
or however your game works.
then late you could check if its visited by doing.
(board piece) visited = 1
-> do this