I am posting the 11 pieces solution shown in the article cited by Michael (it is not freely available online).
This is the smallest known number of pieces. Some remarks:
- The question is open from 4 to 10 for 5, 7, or 9 pieces. Get your pencils!
- Everything so far is with polyominoes. Any suggestion with more complicated shapes?
- Unlike the other solution I posted, this one cannot be resized along the $x$ or $y$ axis.
