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Putnam 2005 A4

Let \(H\) be an \(n \times n\) matrix all of whose entries are \(\pm 1\) and whose rows are mutually orthogonal. Suppose \(H\) has an \(a \times b\) sub matrix whose entries are all \(1\). Show that \(ab \leq n\).

Source: Putnam 2005

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