A277433 Martin Gardner's minimal no-3-in-a-line problem, all slopes version.

1, 4, 4, 4, 6, 6, 8, 8, 8, 8

Offset: 1

Author

Robert Israel, Oct 14 2016

Keywords

• nonn
• more

Comments

a(n) is the minimal number of counters that can be placed on an n X n grid, no three in a straight line, such that adding one more counter on any vacant grid point will produce three in a line. Lines can have any slope.

The "queens" version of this problem, where lines are restricted to vertical, horizontal and diagonal, is A219760.

a(11) <= 10, a(12) <= 10.

Links

• Robert Israel, Examples for n <= 12 (provably optimal for n <= 10).
• Sandi Klavžar, James Tuite, and Ullas Chandran, The General Position Problem: A Survey, arXiv:2501.19385 [math.CO], 2025. See p. 39.

Crossrefs

Cf. A219760.