2.8 lines
Keywords: Theory
Two point eight lines - somewhat amazingly, no more than that is needed to cover half of a 19x19 board along the edges:
The remaining part in the center is equally big.
[edit]
Calculation
180.5 points = 72.0 a + 64.0 b + 44.0 c + 0.5 s
We have to mark the entire first line (72.0 points), then the entire second line (64.0 points), and finally, ca. 0.8 times the third line (0.794643.. * 56.0 points).
(1st) 72.0 / 72.0 = 1.0
(2nd) 64.0 / 64.0 = 1.0
(3rd) 44.5 / 56.0 = 0.794643..
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(sum) 2.794643..
So we get quite exactly 2.8 lines, all in all.
See also