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Place the 35 hexominoes around a circle in such a way that if two of the hexominoes find themselves next to each other, it is because one of the two can be obtained from the other by cutting out one of its component squares (thus obtaining a pentamino) and glueing it elsewhere.

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Here is one possible arrangement (read left to right, top to bottom):
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This construction was fairly loose; I mostly picked unused hexominoes to the end of the sequence and it generally worked out (saving a few long hexominoes for the end) For the last few it is usually possible to "squeeze" a hexomino between two others that transit between a common pentomino.

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