Ultra magic square 9th order

[Natalia Makarova]

There is a solution with magic constant S = 13059 !

[Natalia Makarova]

The solution with magic constant S = 13059 found on the following pattern of residues modulo 5:

3  4  3  4  1  1  1  3  4 
3  3  1  3  4  1  3  1  0 
3  3  3  1  3  1  1  1  3 
3  1  4  3  3  3  1  3  3 
4  3  1  1  1  1  1  4  3 
4  4  1  4  4  4  3  1  4 
4  1  1  1  4  1  4  4  4 
2  1  4  1  3  4  1  4  4 
3  4  1  1  1  3  4  3  4

This pattern is derived from the solution with two errors

2243  2339    83   479   821   761  1031  2843  2459 
1283  1733  2441   293  2729   281  1583  2711     5 
 773  2543  2753  1181  2333    41  2381   101   953 
 593  1601   929  2663   113  2393  1091  1613  2063 
2039   503  1331*  311  1451  2591  1571  2399   863 
 839  1289  1811   509  2789   239  1973  1301  2309 
1949  2801   521  2861   569  1721   149   359  2129 
2897   191  1319  2621   173  2609   461  1169* 1619 
 443    59  1871  2141  2081  2423  2819   563   659

[Natalia Makarova]

I’m trying to find a solution with magic constant S = 13023.
I use the following template of residues modulo 5:

1 1 3 1 2 3 3 1 3
2 2 2 3 2 2 1 3 1
3 3 2 2 3 1 1 1 2
2 1 3 3 1 3 1 2 2
2 2 3 2 2 2 1 2 2
2 2 3 1 3 1 1 3 2
2 3 3 3 1 2 2 1 1
3 1 3 2 2 1 2 2 2
1 3 1 1 2 3 1 3 3

This solution contains only one error.

2851  211 2143  421 1657 1063 1723 2221  733 
  97 2767 1327  523 2857  757 2791  883 1021 
 373 2293 2347 2287 1153 1231 1861  181 1297 
1987 1201 2203 1423   61  163  811 2617 2557 
1747  877  613    7 1447 2887 2281 2017 1147* 
 337  277 2083 2731 2833 1471  691 1693  907 
1597 2713 1033 1663 1741  607  547  601 2521 
1873 2011  103 2137   37 2371 1567  127 2797 
2161  673 1171 1831 1237 2473  751 2683   43

K = 2894, S = 13023

[Autore]

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