Difference between revisions of "2006 Canadian MO Problems/Problem 3"
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==Problem== | ==Problem== | ||
| − | In a rectangular array of nonnegative real numbers with | + | In a rectangular array of nonnegative real numbers with m rows and n columns, each row and each |
| + | column contains at least one positive element. Moreover, if a row and a column intersect in a positive | ||
| + | element, then the sums of their elements are the same. Prove that m = n. | ||
==Solution== | ==Solution== | ||
Revision as of 11:19, 15 August 2008
Problem
In a rectangular array of nonnegative real numbers with m rows and n columns, each row and each column contains at least one positive element. Moreover, if a row and a column intersect in a positive element, then the sums of their elements are the same. Prove that m = n.
Solution
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See also
| 2006 Canadian MO (Problems) | ||
| Preceded by Problem 2 |
1 • 2 • 3 • 4 • 5 | Followed by Problem 4 |
