Four Glasses Puzzle
Four glasses are placed on the corners of a square table. Some of the
glasses are upright (up) and some upside-down (down). A blindfolded
person is seated next to the table and is required to re-arrange the
glasses so that they are all up or all down, either arrangement being
acceptable, which will be signaled by the ringing of a bell.
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 table is rotated through a random angle.
3.The puzzle is to 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 be non-stochastic i.e. it must not depend on luck.
Here is that algorithm!
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 table is rotated through a random angle.
3.The puzzle is to 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 be non-stochastic i.e. it must not depend on luck.
Here is that algorithm!