It is easy to place three dominoes so that each one touches the other two on one side. Figure A gives an example. On the other hand, with four dominoes, no matter how you place them next to each other, there will always be at least two that are not in contact. However, it is possible to find four shapes that can all touch each other. This is the case if we take the four polyominoes of order less than or equal to 3: the monomino (which is nothing other than a small square), a domino and the two possible forms of triominoes, all represented in figure B.
Can you place these four shapes so that each one touches the other three on at least one side?
Note that only contact along the sides is permitted and not just through one corner. Also, the polyominoes must stay in the same plane, you cannot overlap them.
The following question then naturally arises: can we find a polyomino such that four identical copies (within rotations and symmetries) can all touch each other? The answer is yes and the smallest possible example is given by the L-shaped octamino shown in Figure C.
Could you find the configuration allowing four of these octaminos to all be in contact with each other?
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