Problem 6.1. In a $4 \times 4$ square, a chip is placed in the cell marked with a gray background. In one move, the chip moves to an adjacent cell along the direction of the arrow it is on. Additionally, after each move, the arrow in the cell where the chip just was changes to the opposite direction. From which cell will the chip exit the boundary of the square? In your answer, indicate the row and column of this cell.

![](https://cdn.mathpix.com/cropped/2024_05_06_d7ec6e60d14a8fdbf750g-15.jpg?height=367&width=373&top_left_y=404&top_left_x=532)

(a) Row $A$

(1) column 1

(b) Row $B$

(2) column 2

(c) Row $C$

(3) column 3

(d) Row $D$

(4) column 4
Answer: Row $A$, column 2.

Solution. It is easy to see that the chip will follow the route

$$
C 2-C 3-B 3-A 3-A 4-B 4-B 3-C 3-D 3-D 2-C 2-C 1-B 1-A 1-A 2 \text {, }
$$

from cell $A 2$ it will exit the board.