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A concept of a planar modular mechanical metamaterial inspired by the principle of local adaptivity is proposed. The metamaterial consists of identical pieces similar to jigsaw puzzle tiles. Their rotation within assembly provides a substantial flexibility in terms of structural behavior, whereas mechanical interlocks enable reassembly. The tile design with a diagonal elliptical opening allows us to vary elastic properties from stiff to compliant, with positive, zero, or negative Poisson's ratio. The outcomes of experimental testing on additively manufactured specimens confirm that the assembly properties can be accurately designed using optimization approaches with finite element analysis at heart.