A question about factoring and factors

[epsi00]

say we have a number N=pq (known) and we only know the last digits of the two factors p and q ( the righter most digit of each factor ). Is-it possible to determine the other digits of the factors? If not, what is the minimum number of digits that should be known before the answer can be a yes?

 

[mathman]

If N is big enough, I suspect the answer is no.
Let p=100m + r, q=100n + s, where r,s < 100 (all integers).
Then N = 10000mn + 100 (ms + nr) + rs.
You now have one equation (N=) with 2 unknowns (m and n). I don't believe you can find a solution in general.