A puzzle that involves mathematics. Can you solve this mathematical puzzle? Give it a try! Good Luck!! Puzzle 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.
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. Answer: An algorithm that guarantees the bell will ring in at most five turns is as follows:
The puzzle can be generalised to n glasses instead of four. For two glasses it is trivially solved in one turn by inverting either glass. For three glasses there is a two-turn algorithm. For five or more glasses there is no algorithm that guarantees the bell will ring in a finite number of turns. A further generalisation allows k glasses (instead of two) out of the n glasses to be examined at each turn. An algorithm can be found to ring the bell in a finite number of turns as long as k ≥ (1 − 1⁄p )n where p is the greatest prime factor of n. Next Puzzle: A Reclusive Inventor
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