Hard Puzzle
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A stopped clock gives the exact time twice a day, while a normally running (but out of sync) clock will not be right more than once over a period of months. A clever grandfather [as in grandfather clock] adjusted his clock to give the correct time at least twice a day, while running at the normal rate. Assuming he was not able to set it perfectly, how did he do it?
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Using a water tap, a 07 gallon container and a 11 gallon container, can you measure exactly 9 gallons?
You may empty the containers down the drain.
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What if somebody offered to bet that at least two people in your Social group had the same birthday?
Would you take the bet?
How large must a social group be to make the probability of finding two people with the same birthday at least 50%?
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You decide to play a game with your friend where your friend places a coin under one of three cups. Your friend would then switch the positions of two of the cups several times so that the coin under one of the cups moves with the cup it is under. You would then select the cup that you think the coin is under. If you won, you would receive the coin, but if you lost, you would have to pay.
As the game starts, you realize that you are really tired, and you don’t focus very well on the moving of the cups. When your friend stops moving the cups and asks you where the coin is, you only remember a few things:
He put the coin in the rightmost cup at the start.
He switched two of the cups 3 times.
The first time he switched two of the cups, the rightmost one was switched with another.
The second time he switched two of the cups, the rightmost one was not touched.
The third and last time he switched two of the cups, the rightmost one was switched with another.
You don’t want to end up paying your friend, so, using your head, you try to work out which cup is most likely to hold the coin, using the information you remember.
Which cup is most likely to hold the coin?
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