18 Apr '06 19:31>
I apologize if this has been described before (I didn't read all 20 pages of posts before posting this).
The object of this game is to turn four "shot glasses" either all UP or all DOWN. The shot glasses are placed out of sight in the bottom of 4 "pockets" in a special pool table with only 4 pockets (1 in each pocket). Using only your hands (and not peeking inside), you are allowed to reach into any two pockets and flip one or two shot glasses, or simply leave them alone. When you pull your hands out one of two things happen: 1) A bell goes off indicating that all of the glasses are in the same orientation or 2) Not all of the glasses are in the same orientation and the table spins around at incredible speed - the effect of which is that when it stops you do not know which two pockets you just put your hands in.
The problem: What is the minimum number of hand "dips" that are required to guarantee that all of the glasses are in the same orientation? (Fore example: The answer of 1 is not correct because even though you may have been lucky and managed to do it, you couldn't guarantee that you had done it.)
The object of this game is to turn four "shot glasses" either all UP or all DOWN. The shot glasses are placed out of sight in the bottom of 4 "pockets" in a special pool table with only 4 pockets (1 in each pocket). Using only your hands (and not peeking inside), you are allowed to reach into any two pockets and flip one or two shot glasses, or simply leave them alone. When you pull your hands out one of two things happen: 1) A bell goes off indicating that all of the glasses are in the same orientation or 2) Not all of the glasses are in the same orientation and the table spins around at incredible speed - the effect of which is that when it stops you do not know which two pockets you just put your hands in.
The problem: What is the minimum number of hand "dips" that are required to guarantee that all of the glasses are in the same orientation? (Fore example: The answer of 1 is not correct because even though you may have been lucky and managed to do it, you couldn't guarantee that you had done it.)