Ants marching in diagonal lines
There are 81 ants are sitting stable on chessboard on the dark room. Each ant sits on one square. When light is turned on, each ant moves one step diagonally and stop. As a result, several ants will sit on one square and none on others. Find the minimum number of empty squares?
The answer is 9.
This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.
1 solution
The answer is 9 .
Fill the columns of the board alternately by 0's and 1's. As a result, you will get 3 6 0's and 4 5 1's squares. When an ant moves, it will move from 0 t o 1 or 1 t o 0 . It easy to find out that 4 5 − 3 6 = 9 squares will have no ants on them.