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 Aug 17 awarded Popular Question Jan 11 revised Integral solutions to $a_1 \times a_2 \times … \times a_k = N$ Corrected mis-typed constraint Jan 11 revised Integral solutions to $a_1 \times a_2 \times … \times a_k = N$ added 592 characters in body Jan 10 revised Integral solutions to $a_1 \times a_2 \times … \times a_k = N$ added 7 characters in body; edited title Jan 10 asked Integral solutions to $a_1 \times a_2 \times … \times a_k = N$ Nov 12 answered How many matrices are possible for the given arrangement? Nov 12 awarded Scholar Nov 12 accepted How many matrices are possible for the given arrangement? Nov 11 comment How many matrices are possible for the given arrangement? Given that I know the value for m * m matrix. Can this value help me in finding the answer for m * (m + 1), m * (m + 2), ... matrices? Nov 11 awarded Supporter Nov 11 comment How many matrices are possible for the given arrangement? @Robert Israel: m's max value can be 6 and n's max value can be 2^63. Can you tell me how are you able to deduce the matrix based on m's value. Is it some algorithmic technique or just by observing it. Also, can there be derived any recursive relation? Nov 11 comment How many matrices are possible for the given arrangement? How does m fit in this formula? Nov 11 comment How many matrices are possible for the given arrangement? @Pietro Majer: Contiguous means that the rows and columns of the chosen sub-matrix should be adjascent. Nov 11 awarded Student Nov 11 revised How many matrices are possible for the given arrangement? added 11 characters in body Nov 11 comment How many matrices are possible for the given arrangement? What about the case when m = 5 & n = 5 and the matrix is: 0 1 0 1 0 | 0 1 0 1 0 | 0 1 0 1 0 | 0 1 0 1 0 | 0 0 1 1 0 The above is a valid case. Nov 11 comment How many matrices are possible for the given arrangement? @Per Alexandersson: It is evident that we'll have (m - 1) * (n - 1) sub-matrices of order 2 * 2. My strategy is: start picking up 2 * 2 sub-matrices starting from top-left corner i.e. containing cells A(0,0), A(0,1), A(1,0), A(1,1) of main matrix; fill it with 0 and count the total number of matrices having these cells filled in this manner. Now, I proceed on to counting those matrices where the next 2 * 2 matrix i.e. A(0,1), A(0,2), A(1,1), A(1,2) are filled with 0. However, I am not able to count the repeating cases of 2nd matrix which already appeared in the first case. How to achieve this? Nov 11 awarded Editor Nov 11 revised How many matrices are possible for the given arrangement? added 87 characters in body Nov 11 asked How many matrices are possible for the given arrangement?