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

Jun 24, 2016

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Explanation:

Here's one solution:

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Bonus

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.