Blind Bartender’s Problem

Four glasses are placed on the corners of a square Lazy Susan (turntable). Some of the glasses are upright (up) and some upside-down (down).

A blindfolded person is seated next to the Lazy Susan and is required to re-arrange the glasses so that they are all up or all down, either arrangement being acceptable.

The glasses may be re-arranged in turns subject to the following rules.

1. Any two glasses may be inspected in one turn and after feeling their orientation the person may reverse the orientation of either, neither or both glasses.
2. After each turn the Lazy Susan is rotated through a random angle.
3. At any point of time if all four glasses are of the same orientation, a bell will ring.

Can you devise an algorithm which allows the blindfolded person to ensure that all glasses have the same orientation (either up or down) in a finite number of turns? The algorithm must not depend on luck.

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