A blindfolded boy named Scott sits in front of a rotating tray. The tray contains four identical individual glasses. Some are upside down, and others are right side up. However, he is not aware of which is which in this situation. The glasses are placed in rows of two, forming a square.
A bartender named Mary challenges Scott to rearrange all the glasses so that they all match and are all either right side up or upside down. However, he does have some rules to follow.
Any two glasses may be touched in order to see which way they are placed. Mary shall help him locate and touch the
glasses. Scott can go ahead and flip either both glasses, one of them, or flip neither. Mary will then spin the tray to a random number of degrees to provide new and random positions of the glasses.
This will continue until Scott manages to get all four glasses in the same orientation, at which point Mary will let him know. In this scenario, Scott does not want to exceed five turns of the tray before getting the right answer.
What strategy can he use to do this ?
Answer will be provided next Thursday evening after 21:00.
Teaser Of The Day No. 299
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elcarretero
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Re: Teaser Of The Day No. 299
ANSWER
Scott can complete the task in five rounds as follows:
Round 1: Choose any two glasses that are diagonally opposite each other. He will flip both so that they are right side up if they are not already. This will mean that at least two glasses are right side up.
Round 2: Scott will then choose two glasses that are alongside each other (adjacent). At least one will be right side up from the last round. If one of the two adjacent is upside down, turn that one right side up. There are now at least three cups right side up.
Round 3: Scott will now choose two glasses that are diagonally opposite once again. If one is turned downwards, turn it up, and all four glasses will be right side up. If both are right side up, turn one upside down, and there will be two upside-down adjacents to each other.
Round 4: Choose two adjacent glasses and flip them both. If both were the same orientation, then all four glasses will now be flipped the same way. If they were not flipped the same way, there would be two glasses that are upside down diagonally across from each other.
Round 5: Scott will choose any two glasses that are diagonally opposite and reverse both of them. All four glasses will now be the same orientation.
Scott can complete the task in five rounds as follows:
Round 1: Choose any two glasses that are diagonally opposite each other. He will flip both so that they are right side up if they are not already. This will mean that at least two glasses are right side up.
Round 2: Scott will then choose two glasses that are alongside each other (adjacent). At least one will be right side up from the last round. If one of the two adjacent is upside down, turn that one right side up. There are now at least three cups right side up.
Round 3: Scott will now choose two glasses that are diagonally opposite once again. If one is turned downwards, turn it up, and all four glasses will be right side up. If both are right side up, turn one upside down, and there will be two upside-down adjacents to each other.
Round 4: Choose two adjacent glasses and flip them both. If both were the same orientation, then all four glasses will now be flipped the same way. If they were not flipped the same way, there would be two glasses that are upside down diagonally across from each other.
Round 5: Scott will choose any two glasses that are diagonally opposite and reverse both of them. All four glasses will now be the same orientation.
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