Problem 56548. IQpuzzler Challenge #1: Find all possible solutions with 2 pieces already on the board and fixed orientation of all other pieces

Fast and short - impressive!
Still trying to figure out what you are doing...

It's solving the exact cover problem (similar to problem 56588): it defines vectors of zeros and ones representing all possible locations of the pieces (with some extra zeros and ones to make sure each piece is used exactly once), and then uses the Knuth algorithm to find subsets of vectors that add up to all ones.

Thanks for the link! Great inspiration to create more challenges, even though the problem seems to be entirely solved: https://www.ocf.berkeley.edu/~jchu/publicportal/sudoku/0011047.pdf