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

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==Problem==
 
==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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An <math>m \times 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 either <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.
  
  
 
==Solution==
 
==Solution==
 
Coming soon...
 
Coming soon...

Latest revision as of 21:30, 30 December 2021

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

Coming soon...

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