I'm trying to prove that all valid $n^2 \times n^2$ Sudoku solutions follow a cyclic permutation pattern for a subset of $n!$ Sudoku grids.
But, I'm not sure on how to prove it.
Let $n$ be any input length with non-repeating elements.
For $n$ in range shift as follows,
$n$ = 123456789
123456789 456789123 789123456 234567891 567891234 891234567 345678912 678912345 912345678
Now, suppose I try a different input following the same cyclic pattern
$n$ = 987654321
987654321 654321987 321987654 876543219 543219876 219876543 765432198 432198765 198765432
for $S = n>> ∞ $,
Given valid solved $n^2 \times n^2$,
$X!$ amount can be generated in $O(n)$ time given any input of non-repeating elements Do not confuse with O(1) time because the bigger the element the more bits it needs!!! Thus, the more time it takes to execute!
I'm not familiar with mathematics, and I'm looking to be pointed in the right direction. How would I prove that this works for ALL $n^2\times n^2$ Sudoku Solutions?