Jigsaw puzzles are awesome and making them is an easy way to get rich. So I bought a cutting machine to make puzzles. Unfortunately I could only afford the cheapest machine available. All pieces are arranged in the standard rectangular pattern, no fancy shapes or arrangements.
Additionally the machine can only do a single shape for the tap and the blank. That means any two pieces with a tap and a blank fit together.
I still want to have my puzzles a unique correct solution. So in spite of the individual pieces fitting together in lots of ways there should be only one way to arrange all pieces into a rectangle.
Question: What is the biggest puzzle in terms of number of pieces I can make?
Here are two examples of puzzles I could make with the machine. Any individual piece can be described by listing the four sides in clockwise order. Each can be a (s)ide, a (t)ap or a (b)lank.
Puzzle A consists of the four pieces (s,s,t,t), (s,s,t,b), (s,s,b,t) and (s,s,b,b). This can be assembled as a 2 by 2 puzzle in a unique way (up to rotation). This is a good puzzle.
Puzzle B consists of the four pieces (s,s,t,t), (s,s,t,b), (s,s,t,b) and (s,s,b,b). This can be assembled as a 2 by 2 puzzle in two distinct ways. So there is no unique solution and I don't want that.
PS: This can be solved with pen and paper, no computer required. If someone wants to make helpful pictures feel free to edit.
Edit in response to comments: If a piece can be rotated in place the picture would still be off so that would count as distinct ways to assemble. Sides are only on the boundary, not inside the puzzle.