As shown in the figure, chess pieces are placed at the intersection points of the 64 grid lines of the 7×7 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 combinatoricscombinatorial geometry