Problem of the Week

Aug. 22, 2020 to Aug. 29, 2020

A lock has 16 keys arranged in a 4x4 array, each key oriented either horizontally or vertically. In order to open it, all the keys must be vertically oriented. When a key is switched to another position, all the other keys in the same row and column automatically switch their positions too. Show that no matter what the starting positions are, it is always possible to open this lock. (Only one key at a time can be switched.)

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