You have three flat pieces, as shown:
Arrange them flat, without overlap, such that the shape formed by the black parts is congruent to the shape formed by the white parts. Rotation and reflection are allowed.
Find at least 7 distinct solutions.
If you find a single one, feel free to post a partial.
Quick note to clarify the aim of this puzzle: This is not a trick question where you need to stack the shapes/make a 3d shape etc. It's exactly what it appears to be. The solutions are just really hard to find.
Answer
8th one’s a charm, and might well be the sparsest solution without oblique rotations:
Equivalent independent earlier posts:
1. P.-S. Park
3, 4, 6. akhilesh
Solutions 7−12 have vector-like annotations, such as [-2B -1B 2x 2y ] for solution 12, because they can be generated formulaically.
Such configurations can be rotated 90° counter-clockwise to match single squares, A with A', and double squares, B with B' and C with C'. The orientation of the L-shaped piece is determined by ± 2B and ±1B while the S-shaped piece is oriented by ± 2x and ± 2y. This generates 16 configurations but some of them are invalid due to overlapped pieces. (In fact, [2B 1B 2x 2y ] produces an overlap and is inaccurately shown in the diagram.)
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