Consider a 5×5 square divided into 25 cells. Initially all cells are white. In each move it is allowed to change the colour of any three consecutive cells in a row or column to the opposite colour (i.e. white cells become black and black ones become white). What is the minimum possible number of moves needed to obtain the chessboard colouring shown in the figure?
A friend and I were able to show that 16 moves can create the chessboard under the given conditions. However, we weren't able to prove that 16 is the minimum possible number of moves that can create the chessboard. Upon checking the internet for possible solutions to the problem, we found out that the minimum possible number of moves is less than 10, according to the answer key accompanying the exam from which the question was extracted (KSF 2016, Student Level, Question 29). However, we have no idea how this answer was obtained.