A280537 - OEIS

%I #17 Oct 27 2017 13:02:04

%S 5,8,10,13,16,18,20

%N Maximum number of points that can be selected from an n X n X n grid so that no four of them are in a plane.

%C Terms up to a(6) were found by exhaustive search. a(7) and a(8) are based on extensive numerical evidence.

%C Currently (January 2017) known lower bounds for the next terms are a(9)>=23, a(10)>=26, a(11)>=28, a(12)>=30, a(13)>=32, a(14)>=35, a(15)>=36, a(16)>=38, a(17)>=42.

%D Walter Möhres, Exhaustive Search for the 6x6x6 "No Four in Plane Problem". Private communication, September 2016.

%H Ed Pegg Jr, <a href="http://demonstrations.wolfram.com/NoFourInPlaneProblem/">No-Four-In-Plane Problem</a>, Wolfram Demonstrations Project.

%H Ed Pegg, <a href="http://math.stackexchange.com/questions/553431/no-four-in-plane-can-11-points-be-picked-from-a-4-times4-times4-grid">No-Four-In-Plane, can 11 points be picked from a 4 X 4 X 4 grid?</a>. Question in Mathematics Stack Exchange, a(4) and a(5) provided in answers.

%H Torsten Sillke, <a href="https://groups.google.com/forum/#!topic/rec.puzzles/pLH_gZeItq8">no 4 on a plane (3*3*3 puzzle)</a>, discussion in newsgroup rec.puzzles, Nov 27, 1992.

%H Al Zimmermann's Programming Contests, <a href="http://azspcs.com/Contest/Tetrahedra">Non-Coplanar Points</a>, March - June 2016.

%Y Cf. A000769, A272651, A280538.

%K nonn,more,hard

%O 2,1

%A _Hugo Pfoertner_, Jan 05 2017