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I think it can be done with brute force / backtracking - I wonder if there is some other nicer / optimized solution...
The problem is when N1, N2 are larger than 10 and we achieve for check the base...

I wrote yesterday:

"Consider in some base B numbers of N1 x N2 digits, N1 "groups" each made by N2 digits.
(for ex. N2=8 & B=2 we have N1 "octets")
For all pairs of 2 digits in any 2 positions...

Consider in some base B numbers of N1 x N2 digits, N1 "groups" each made by N2 digits.
(ex.N2=4 we have N1 "octets")
For all pairs of 2 digits in any 2 positions let say i,j as b_i,b_j in the same...