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

1 Answer
George C.
Jun 24, 2016

See explanation...

Explanation:

Here's one solution:

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#color(white)()#
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.

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