Question

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

Answer 1

See explanation...

Explanation:

Here's one solution:

`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.