Start with a square. Any side of the square can be either straight or have an interlocking pattern, as shown in the two examples below:
That gives $2 \times 2 \times 2 \times 2 = 16$ possible squares.
Is it possible to create a $4 \times 4$ jigsaw puzzle (outside borders straight) with these $16$ pieces? Rotation or flipping of pieces is not allowed.