The 6 illustrated matches are all touching. But can you arrange them so that each match touches all the others? (You might be better trying this with actual matches.) |
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The solution can be illustrated on this page, but you will need to think beyond the plane. Illustrate the solution in two parts, each in a separate plane.
Place the matches in two sets of 3, all 3 touching as above. Then place one set on top of the other. This problem is often posed with cigarettes. There is actually a solution with 7 cigarettes, all touching, with a central cigarette standing on its end.