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October 2022 - Solution

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October 2022 Challenge

October 2022 Solution:

The best solution (132) was found by many solvers. Here is the last one submitted, by Radu-Alexandru Todor:
4 2 6 3 5 1
5 6 1 4 3 2
3 1 5 2 4 6
2 3 4 1 6 5
1 5 3 6 2 4
6 4 2 5 1 3

5 3 1 4 6 2
6 4 2 5 1 3
1 5 6 3 2 4
3 1 5 2 4 6
2 6 4 1 3 5
4 2 3 6 5 1

6 1 5 2 4 3
1 5 3 6 2 4
2 6 4 1 3 5
4 2 6 3 5 1
3 4 2 5 1 6
5 3 1 4 6 2

3 4 2 5 1 6
4 2 6 3 5 1
5 3 1 4 6 2
1 5 3 6 2 4
6 1 5 2 4 3
2 6 4 1 3 5

2 6 4 1 3 5
3 1 5 2 4 6
4 2 3 6 5 1
6 4 2 5 1 3
5 3 1 4 6 2
1 5 6 3 2 4

1 5 3 6 2 4
2 3 4 1 6 5
6 4 2 5 1 3
5 6 1 4 3 2
4 2 6 3 5 1
3 1 5 2 4 6
132

In the bonus part, all 34 diagonals can be achieved, and given this 84 is the maximal solution, given by
0 0 0 0 0
1 1 1 1 1
2 2 2 2 2
3 3 3 3 3
4 4 4 4 4

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

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

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

2 2 2 2 2
0 0 0 0 0
4 4 4 4 4
1 1 1 1 1
3 3 3 3 3
84