How can you arrange 7 dots so that there are 6 lines of 3 colinear dots?

1 Answer
George C.
Jun 24, 2016

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Explanation:

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This is an example of a problem that is very difficult to solve in the general case. The maximum number lines of 3 dots in n dots follows the sequence (catalogued as A003035 in the online encyclopedia of integer sequences) that starts:

0, 0, 1, 1, 2, 4, 6, 7, 10, 12, 16, 19, 22, 26

The next number in the sequence is known to be 31 or 32, but it is an unsolved problem which one it is.

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