I have sixteen counters which are black on one side and white on the other. They are arranged in a 4‐by-4 square. Initially, all the counters are facing black side up.
In one move, we must choose a 2‐by‐2 square within the square and turn all four counters over. For example, we could turn all four counters in this squares.
Describe a sequence of moves of minimum length that turns the initial configuration into one where the counters alternate in colour, asshown below.
How many moves do you need at least? Type in the number here ______