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Difference between revisions of "1998 IMO Shortlist Problems/C1"

(Created page with " An m x 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 [x] or [x] + 1, so that the row and column...")
 
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An m x 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 [x] or [x] + 1, so that the row and column sums are unchanged.
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==Problem==
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An <math>m x n</math> array of real numbers has the sum of each row and column integral. Show that each non-integral element <math>x</math> can be changed to <math>\left\lfloor x \right\rfloor</math> or <math>\left\lfloor x \right\rfloor + 1</math>, so that the row and column sums are unchanged.
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==Solution==
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Coming soon...

Revision as of 22:29, 30 December 2021

Problem

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


Solution

Coming soon...

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