Question 14
As shown in the diagram on the left below, there are six identical black circles in the first row of a $6\times6$ chessboard and six identical white circles in the last row. The circles can move one at a time, horizontally, vertically or diagonally (parallel to the main diagonals) by any number of squares as long as no other circle blocks the path. Black and white circles move alternately. What is the minimum number of moves required to interchange the black and white circles as shown in the diagram on the right below? You must prove that achieving the goal in fewer moves is impossible and provide one sequence of moves that accomplishes the interchange using the minimum number of moves.
Give a sequence of moves that accomplishes the interchange. The source provides 30 identical blank boards for recording moves; one reusable template is shown here.
Give a sequence of moves that accomplishes the interchange. The source provides 30 identical blank boards for recording moves; one reusable template is shown here.