Each time you can switch the black ( B ) / white ( W ) colour for a whole row or a whole column of 4 * 4 board below
W B W W
W B B B
W B W W
B W B W
Can you switch the colours so that all the squares are black?
2007-03-10 17:59:11 · 1 個解答 · 發問者 鴻佳 4 in 科學 ➔ 數學
No for this particular layout.
Proof:
Every time you switch a row, the number of white (or Black) squares will be increased (or decreased) by an even number of squares (-4,-2,0,2, or 4). Since there are 7 Black squares to start with, and we want to end up with 16, it will not be possible to do so by flipping whole columns or rows.
2007-03-10 18:29:52 · answer #1 · answered by p 6 · 0⤊ 0⤋