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

1,2

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

Table of n, a(n) for n=1..10.

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.

Sequence in context: A073229 A116446 A102126 * A219760 A097918 A256416

Adjacent sequences: A277430 A277431 A277432 * A277434 A277435 A277436

Keyword

nonn,more

Author

Robert Israel, Oct 14 2016

Status

approved