348. The Cabinetmaker's Problem. A cabinetmaker had a $7 \times 7$ chessboard piece made of excellent plywood, which he wanted to cut into 6 pieces so that they could be used to form 3 new squares (all of different sizes).

How should he proceed, without losing any material and making cuts strictly along the lines?
348. The figure shows how a piece of plywood can be cut. Squares \(A\) and \(B\) are cut out entirely (1), and from the four pieces \(C, D\), \(E\) and \(F\), a third square can be formed (2).

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-269.jpg?height=442&width=397&top_left_y=961&top_left_x=658)

2

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-269.jpg?height=331&width=346&top_left_y=1071&top_left_x=1072)

[There are solutions to this problem that involve only five pieces. Could the reader find a solution with five pieces where the total length of the cuts is 16 units \(3-M . \Gamma\).]