Carpet cutting puzzle
by Jan Kristian Haugland

The following puzzle dates back to Sam Loyd (1908):

Cut a 7×7 carpet into five pieces in such a way that the pieces can be put together to form
a 6×6, a 3×3 and a 2×2 carpet. The pieces can be rotated but not flipped over (mirrored).

With computer aid I have found that there are 246 solutions, assuming that the cuts must be along the grid lines.

List of solutions (txt)

List of solutions (html)

Solutions by cut length (html)

Some curious solutions:	No. 024 does not contain a 2×2 piece.
	No. 101 does not contain a piece of size greater than 12.
	No. 104 consists of rectangles only.

Here is a similar puzzle. Cut a 6×6 carpet into three pieces in such a way that
the pieces can be put together to form a triangle with base 8 as seen in the figure:

There are only two solutions (same assumption as above).