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Problem #17

Magical Matrix

Let 0 < t < u < v, where t, u and v are integers. Now, there is a matrix Q with three rows and c columns where c > 1. The matrix is special in a way that each of its columns contains the three numbers t, u and v in some order. All the 3 numbers must appear in every column. Sum of all numbers in row 1 is 20, sum in row 2 is 10 and in row 3, the sum is 9. The rows are numbered 1, 2, 3 while columns are numbered 1,2,..,c and each cell in the matrix is denoted by a pair (i,j), where i=row & j=column. Now the cell (2,c) contains v.

Calculate ∑ [Q_{i,j} × (i+j)] for the whole matrix.

Contributed by Varun Syal

Solved by 322 users

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