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Prove that I can choose exactly one $\mathbf{1}$ from each row such that for every two of them,they are not in the same column.

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    See [Hall’s marriage theorem](http://en.wikipedia.org/wiki/Hall%27s_marriage_theorem).2012-09-26
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    Please edit the question so the question is in the body, not just in the title.2012-09-27

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