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In each cell of an \(n \times n\) chessboard there is a lamp. When a lamp is touched, the state of this lamp and all the lamps in its row and its column is changed. Initially all the lamps are off. Show that it is always possible to turn on all the lamps with finitely many touches, and find in terms of \(n\) the minimum number of touches needed.
in Mathematics by Platinum (138,598 points) | 28 views

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