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You are presented with two identical envelopes, each containing money. One envelope has twice as much money as the other. You are allowed to choose one envelope and keep the money it contains.
After you choose an envelope, you are given the option to switch to the other envelope. Should you switch? Is there a strategy that gives you the highest chance of getting the envelope with the most money?
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Five prisoners, two men and three women were made to sit around a pentagonal table. The warden comes and places a fruit on each one’s head such that the prisoners do not know the type of fruit on their heads but they can see the fruits on the head of the others.
They were told that the fruits are either apple or orange and there are at least two fruits of each types.
Then how many of them can deduce the exact fruit on their heads if they are not allowed to communicate with each other?
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You are given nine coins, one of which is fake and is either lighter or heavier than the others. You have a balance scale that you can use only twice. How can you identify the fake coin and determine whether it is lighter or heavier than the others using only two weighings?