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Lateral Thinking #20- The Four Glasses -

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Puzzle Image A blindfolded boy, Milo, sits before a rotating tray on which there are four identical glasses. Some are right side up and some are upside down. The orientation of the glasses is unknown to him (the image shown is for illustration only). The glasses are positioned in an imaginary two by two grid (so there's a glass in the top-left, top-right, bottom-left, and bottom-right of the rotating tray). A bartender, Katie, challenges Milo to rearrange the orientation of the glasses so that all four are either face up or face down. The rules are as follows. Any two glasses may be touched to check their orientation. Katie will help Milo locate and touch specific glasses (e.g. in the top-left and top-right on the tray). Milo may then flip either, neither, or both glasses. Katie will then spin the rotating tray a random number of degrees resulting in a new position. Then, another round will begin with the same rules as before. This will continue until Milo manages to get all four glasses in the same orientation (at which point Katie will let him know that he has accomplished the task).

There is a very particular strategy that will ensure that all glasses are in the same orientation by no later than the fifth round? Can you figure it out? Check the hint if you need a clue. Note that this is not a trick question (e.g. Milo cannot take off the blindfold, ask questions about the glasses, enlist the help of anyone else, etc.)

Do you have a suggestion for this puzzle (e.g. something that should be mentioned/clarified in the question or solution, bug, typo, etc.)?