Я нашёл не строго диагональное решение C8N57. Если заменить одну диагональ (5ую) то получится строгое.
It is clear, that such a solution exists. A nonstrict diagonal solution (which is not derived from deleting rows and columns) exists always, if C= primepower+1 and N=C^2+C+1. In this case we have one diagonal, where all C colors are possible for each cell. In the example below, you can use any color you want for each cell of the the 5.th diagonal. This example derives from the CDS {0, 1, 3, 13, 32, 36, 43, 52}.
(Оффтоп)
6,3,3,2,3,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,
3,3,2,3,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,
3,2,3,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,
2,3,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,
3,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,
1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,
2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,
1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,
5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,
8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,
8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,
6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,
8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,
7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,
3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,
5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,
2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,
1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,
7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,
7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,
6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,
7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,
8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,
4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,
5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,
6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,
6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,
4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,
6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,
5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,
5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,
7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,
5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,
3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,
4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,
2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,
1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,
3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,
6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,
2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,
1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,
8,5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,
5,4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,
4,3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,
3,8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,
8,2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,
2,1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,
1,4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,
4,4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,
4,7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,
7,4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,
4,8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,
8,3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,
3,7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,
7,2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,
2,1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,
1,6,3,3,2,1,1,2,1,5,8,8,6,8,7,3,5,2,1,7,7,6,7,8,4,5,6,6,4,6,5,5,7,5,3,4,2,1,3,6,2,1,8,5,4,3,8,2,1,4,4,7,4,8,3,7,2
So there also exists a nonstrict diagonal solution for C9N73 and C10N91. I also made the 5. diagonal arbitrary.
C9N73, derived from CDS {0, 1, 3, 7, 15, 31, 36, 54, 63}:
(Оффтоп)
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I do not post C10N91 here, it is too large.