Coin in the Bottle

I inserted a coin in a bottle and closed its mouth with the help of a cork. Now, I was able to take the coin out from the bottle without taking out the cork or breaking the bottle. Can you tell me how I did it?




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The warden meets with 23 new prisoners when they arrive. He tells them, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another.

"In the prison is a switch room, which contains two light switches labeled 1 and 2, each of which can be in either up or the down position. I am not telling you their present positions. The switches are not connected to anything.

"After today, from time to time whenever I feel so inclined, I will select one prisoner at random and escort him to the switch room. This prisoner will select one of the two switches and reverse its position. He must flip one switch when he visits the switch room, and may only flip one of the switches. Then he'll be led back to his cell.

"No one else will be allowed to alter the switches until I lead the next prisoner into the switch room. I'm going to choose prisoners at random. I may choose the same guy three times in a row, or I may jump around and come back. I will not touch the switches, if I wanted you dead you would already be dead.

"Given enough time, everyone will eventually visit the switch room the same number of times as everyone else. At any time, anyone may declare to me, 'We have all visited the switch room.'

"If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will all die horribly. You will be carefully monitored, and any attempt to break any of these rules will result in instant death to all of you"

What is the strategy they come up with so that they can be free?

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John and Jenni are a married couple. They have two kids, one of them is a girl. Assume safely that the probability of each gender is 1/2.
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Hint: It is not 1/2 as you would first think.

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I have lakes with no water, mountains with no stone and cities with no buildings. What am I?

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If nine thousand, nine hundred nine dollars is written as $9,909,
how should twelve thousand, twelve hundred twelve dollars be written?

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You need to climb ten stairs. At every stair, you can either take one step up or you can jump two steps up.

In how many different ways you can climb 10 stairs?

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Find The Next Number in this series.
1, 2, 6, 42, 1806 ?

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