n all . / - : x c o + * sum
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1 0 0 0 0 0 0 0
2 1 0 0 0 0 0 0 0 1 1
3 2 0 0 0 1 1 1
4 11 0 0 1 1 1 0 0 1 4
5 32 3 2 0 0 0 5
6 50 4 0 0 2 2 3 0 0 11
7 132 11 1 10 0 0 22
8 380 40 5 1 7 0 4 0 0 57
9 368 41 3 7 0 1 51
10 1135 132 3 0 13 1 6 0 1 156
11 1120 122 6 30 0 0 158
12 4348 524 3 0 33 2 4 0 0 566
13 3622 407 9 82 1 0 499
14 10568 1284 5 0 61 3 13 0 0 1366
15 30634 3681 13 283 1 0 3978
16 46304 5683 14 0 189 1 13 0 0 5900
17 55576 6800 12 282 0 1 7094
18 152210 18853 14 0 328 2 7 0 0 19204
19 258176 31967 16 594 0 2 32577
20 941580 117347 17 0 675 2 16 0 0 118057
21 .. .. 13 2413 0 1 ..
22 .. 18 0 1248 1 8 0 0 ..
23 .. 34 3968 1 1 ..
24 .. 43 0 2852 2 23 0 0 ..
25 .. 55 8983 2 3 ..
26 .. 42 1 4870 0 36 0 0 ..
27 .. 44 17341 0 9 ..
28 .. 1 12085 0 58 0 0 ..
29 .. 44828 1 8 ..
30 .. 0 1 92 0 0 ..
31 .. 2 5 ..
32 .. 0 1 101 0 0 ..
33 .. . 0 14 ..
34 .. 0 0 172 0 0 ..
35 .. 1 23 ..
36 .. 0 1 281 0 0 ..
37 .. 0 21 ..
38 .. 1 337 0 0 ..
39 .. 0 33 ..
40 .. 0 541 0 0 ..
41 .. 0 35 ..
42 .. 1 746 0 0 ..
43 .. 0 63 ..
44 .. 1 1016 0 0 ..
45 .. 0 106 ..
46 .. 0 1366 0 0 ..
47 .. 1 105 ..
48 .. 0 2124 0 0 ..
49 .. 0 196 ..
50 .. 0 3381 0 0 ..
51 .. 0 264 ..
52 .. 0 5062 0 0 ..
53 .. 0 377 ..
54 .. 7696 0 0 ..
55 .. 573 ..
56 .. 10441 0 0 ..
57 . . .
58 .. .. 0 0 ..
59 . . .
60 .. .. 0 ..
61 . . .
62 .. .. 0 ..
63 . . .
64 .. .. 0 ..
65
66 .. .. 0 ..
67
68 .. .. 0 ..
The column with heading * continues to be 0 for all n <= 98 .
======================= last updated: 21. May 2026 ========================
Explanation to the entries:
---------------------------
A number in the apropriate place gives the number of all existing solutions.
. instead of a number means one known configuration.
.. means some known configurations.
Heading abbreviations:
----------------------
n grid size
all total #
. # with no symmetry
/ # with exactly one diagonal reflection symmetry
- # with exactly one orthogonal reflection symmetry
: # with exactly half rotation symmetry
x # with exactly both diagonal reflection symmetries
c # with quarter rotation symmetry except long diagonals
thus the true symmetry is either : or x (if n=3)
o # with quarter rotation symmetry, but not fully symmetrical
+ # with exactly both orthogonal reflection symmetries
* # with all 8 symmetries of the grid, i.e. fully symmetrical
sum # which are not equivalent under symmetry transformation
read # as number of solutions of the No-Three-in-Line-Problem
Thus all solutions for a given symmetry class up to grid size n are known:
all . / - : x c o + *
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n 20 20 27 36 29 53 55 56 58 98