MathDB

As shown in the figure, chess pieces are placed at the intersection points of the

64

grid lines of the

7\times 7

grid table. At most

1

piece is placed at each point, and a total of

k

left chess pieces are placed. No matter how they are placed, there will always be

4

chess pieces, and the grid in which they are located the points form the four vertices of a rectangle (the sides of the rectangle are parallel to the grid lines). Try to find the minimum value of

k

. https://cdn.artofproblemsolving.com/attachments/5/b/23a79f43d3f4c9aade1ba9eaa7a282c3b3b86f.png

Problem Statement