MathDB
Sums in a Matrix

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January 18, 2009
linear algebramatrix

Problem Statement

The three row sums and the three column sums of the array [492816357]\begin{bmatrix} 4 & 9 & 2 \\ 8 & 1 & 6 \\ 3 & 5 & 7 \end{bmatrix} are the same. What is the least number of entries that must be altered to make all six sums different from one another?
<spanclass=′latex−bold′>(A)</span> 1<spanclass=′latex−bold′>(B)</span> 2<spanclass=′latex−bold′>(C)</span> 3<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 5 <span class='latex-bold'>(A)</span>\ 1\qquad <span class='latex-bold'>(B)</span>\ 2\qquad <span class='latex-bold'>(C)</span>\ 3\qquad <span class='latex-bold'>(D)</span>\ 4\qquad <span class='latex-bold'>(E)</span>\ 5
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