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A milk crate holds 24 bottles in four rows and six columns. Can you put 18 bottles of milk in the crate so that each row and each column of the crate have an even number of bottles in it?

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Yes.

$\begin{array}{ccc} B&B&B&.&.&B\\ B&B&B&.&B&.\\ B&B&B&B&B&B\\ B&B&B&B&.&. \end{array}$

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    So @Mark, should I ask my generalization as a new question so you can have a chance to shine?2012-10-04