Arrange pennies on a 4 by 4 square such as this one so that they make the pattern shown. Keep another eight pennies on hand; they will be needed later. The object of this challenge problem is to fill up all 16 squares with pennies. A valid move is to add or remove pennies from four squares whose corners meet at a lettered intersection so that the empty squares are filled, and the full squares are emptied (within the four squares that share a corner).

For example, we could choose the four squares around E. We notice that the upper left and lower right squares are full. A valid move would be to change the arrangment so that the upper right and lower left squares are full and the other two are empty. If the configuration of the board allows, you may (for example) make a change which will remove one penny but will add three more, and you will need to use the extra pennies.

What is the least number of moves required to fill all 16 squares? (Show your work)

And the answer is...