IMO Shortlist 1998 problem C1

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Dodao/la: arhiva
2. travnja 2012.
A rectangular array of numbers is given. In each row and each column, the sum of all numbers is an integer. Prove that each nonintegral number x in the array can be changed into either \lceil x\rceil or \lfloor x\rfloor so that the row-sums and column-sums remain unchanged. (Note that \lceil x\rceil is the least integer greater than or equal to x, while \lfloor x\rfloor is the greatest integer less than or equal to x.)
Izvor: Međunarodna matematička olimpijada, shortlist 1998