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1998 IMO Shortlist Problems/C1

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Problem

An $m \times n$ array of real numbers has the sum of each row and column integral. Show that each non-integral element $x$ can be changed to either $\left\lfloor x \right\rfloor$ or $\left\lfloor x \right\rfloor + 1$ so that the row and column sums are unchanged.


Solution

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