A280537 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.

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

Offset: 2

Author

Hugo Pfoertner, Jan 05 2017

Keywords

• nonn
• more
• hard

Comments

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

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.

References

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

Links

• Ed Pegg Jr, No-Four-In-Plane Problem, Wolfram Demonstrations Project.
• Ed Pegg, No-Four-In-Plane, can 11 points be picked from a 4 X 4 X 4 grid?. Question in Mathematics Stack Exchange, a(4) and a(5) provided in answers.
• Torsten Sillke, no 4 on a plane (3*3*3 puzzle), discussion in newsgroup rec.puzzles, Nov 27, 1992.
• Al Zimmermann's Programming Contests, Non-Coplanar Points, March - June 2016.

Crossrefs

Cf. A000769, A272651, A280538.