Dissection puzzles
by Jan Kristian Haugland

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

Dissect a 7×7 square into five pieces, and reassemble the pieces into a 6×6, a 3×3
and a 2×2 square. 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

Solutions sorted by cut length

Here is a similar puzzle. Dissect a 6×6 square into three pieces, and reassemble the pieces into a triangle with base 8 as seen in the figure:

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

The corresponding puzzle with hexagonal cells has 41 solutions.