Translational tiling of the plane with a set of four (disconnected) polyominoes is undecidable.
Berger, The undecidability of the domino problem,Memoirs of the American Mathemat- ical Society,66(1966), 1-72
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Undecidability of Translational Tiling of the Plane with Four Tiles
Translational tiling of the plane with a set of four (disconnected) polyominoes is undecidable.