Aug 042017
 

You may solve the simple probability, “Given a set of n randomly chosen people, what is the probability of two people having same birthday?”

You may also solve,  “At least how many people need to be picked to make the probability 100% that at least two of them have same birthday?”

Answer to the second question is 367, because there are 366 possible birthdays (including Feb-26).

The question now is, “At least how many people need to be picked to make the probability 99.9% that at least two of them have same birthday?”

Answer is 70.

And if the question is,“At least how many people need to be picked to make the probability 50% that at least two of them have same birthday?”

Answer is 23.

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Aug 022017
 

Doctor gave you two types of medicine tablets (pils) A and B, and asked you to take one from each daily. The two tablets are in different bottles and look exactly same

One day, while taking the pills, you open Bottle-A and tap one pill out in your hand. Then you open the second bottle to take one pill from it, but accidentally two pills pop out from the bottle on your hand. Now you have 1 A-Pill and 2 B-Pills in your hand and you cannot distinguish them.

The pills are very expensive and you do not want to throw them, neither can you afford to take wrong pills. What should you do?
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May 122016
 

You are blindfolded and 10 coins are place in front of you on table. 5 are having their heads-side up and 5 are having their tails-side facing upward.

You cannot tell which way they are by touching the coin.

You are allowed to touch the coins and flip them as many times as you want.

How do you make two piles of coins each with the same number of heads-up and tails-up?
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Sep 282015
 

There are 10 prisoners are in 10 different cells of a prison. There is no way in which they can communicate with each other.

Each night, the warden picks one of the 10 prisoners and that prisoner is supposed to spend the entire night in the central living room. There is one bulb in the living room which can be switched on or off.

Warden puts a condition, “If any of the prisoner can tell with certainty, that all the other prisoners have spent night in the central living room, then he will free all of them. But, If the prisoner says that all the other have spent night in the living room, but that is not true, then all the prisoners will be killed”. Thus, the assertion should only be made if the prisoner is 100% certain of its validity.

Before the random picking begins, the prisoners are allowed to get together and make some strategy. But, once the strategy is made, then a prisoner cannot communicate with any other prisoner.

What plan should they agree on, so that eventually, someone will make a correct assertion?
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Sep 242015
 

Four glasses are placed on the four corners of a square rotating table. Each glass is either upright (up) or upside-down (down). You have to turn all the glasses in same direction (either all up or all down). There are following conditions

  1. You are blindfolded,
  2. At one time you can only change two glasses (and you cannot touch other two glasses).
  3. The table spins after each time you change the glasses.

When all the glasses comes in one direction, then a bell rings and the game stops?
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Sep 242015
 

You are standing before two closed doors. One of the doors leads to heaven and the other one leads to hell.

Two watchmen are standing, one in front of each door. You know one of them always tells the truth and the other always lies, but you don’t know which watchman tells the truth and who is the liar.

You can ask only one question to one of them, in order to find the way to heaven. What will you ask?
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Jul 012015
 

You have some work to be done by a worker in 7 days. The worker need to be paid every day after his work. The total cost of the work of 7 days is one gold bar (so every day the worker must be paid 1/7’th of the bar).

You have only one gold bar, and you can make only two cuts in that bar. How will you ensure that the worker is paid every day? Continue reading »