"Enjoy The Puzzles"

Q1:
A person who was making a list of population of NOIDA came to RAM’s house and that man wants to record the age of all people staying with RAM. That man was RAM’s childhood friend meeting after a longtime.
RAM’S FRIEND: "How have you been?"
RAM: "Great! I got married and I have three daughters now.
"RAM’S FRIEND: "Really? How old are they?"
RAM: "Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..."
RAM’S FRIEND: "Right, ok... Oh wait... Hmm, I still don't know."
RAM: "Oh sorry, the oldest one just started to play the piano."
RAM’S FRIEND: "Wonderful! My oldest is the same age!"

Q2:
Five pirates discover a chest full of 100 gold coins. The pirates are ranked by their years of service, Pirate 5 having five years of service, Pirate 4 four years, and so on down to Pirate 1 with only one year of deck scrubbing under his belt. To divide up the loot, they agree on the following:
The most senior pirate will propose a distribution of the booty. All pirates will then vote, including the most senior pirate, and if at least 50% of the pirates on board accept the proposal, the gold is divided as proposed. If not, the most senior pirate is forced to walk the plank and sink to Davy Jones’ locker. Then the process starts over with the next most senior pirate until a plan is approved.
Remember that these pirates are not ordinary people they are extremely intelligent and greedy, they are also perfectly rational and know exactly how the others will vote in every situation. Emotions play no part in their decisions.
The most senior pirate thinks for a moment and then proposes a plan that maximizes his gold, and which he knows the others will accept. How does he divide up the coins?

Q3:
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 A and B, each of which can be in either the 'on' or the 'off' 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 move one, but only one of the switches. He can't move both but he can't move none either. Then he'll be led back to his cell
"No one else will enter the switch room until I lead the next prisoner there, and he'll be instructed to do the same thing. 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.
"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. At any time anyone of you may declare to me, 'We have all visited the switch room.' and be 100% sure.
"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 be fed to the alligators."
What is the strategy they come up with so that they can be free?

Q4:
you are presented with three doors (door 1, door 2, door 3). one door has a million dollars behind it. the other two have goats behind them. you do not know ahead of time what is behind any of the doors.
monty asks you to choose a door. you pick one of the doors and announce it. monty then counters by showing you one of the doors with a goat behind it and asks you if you would like to keep the door you chose, or switch to the other unknown door.
should you switch? if so, why? what is the probability if you don't switch? what is the probability if you do.

Q5:
There is a pile of N (can be Even or Odd) coins placed on a table, in which K coins head upward. Can you make two piles of coin out of this pile having equal number of heads upward? But you can’t see which coin is heading upward, you can just count coins. No restriction on K

Q6:
"a line of 100 airline passengers is waiting to board a plane. they each hold a ticket to one of the 100 seats on that flight. (for convenience, let's say that the nth passenger in line has a ticket for the seat number n.)
unfortunately, the first person in line is crazy, and will ignore the seat number on their ticket, picking a random seat to occupy. all of the other passengers are quite normal, and will go to their proper seat unless it is already occupied. if it is occupied, they will then find a free seat to sit in, at random.
what is the probability that the last (100th) person to board the plane will sit in their proper seat (#100)?"

Q7:
"at one point, a remote island's population of chameleons was divided as follows:
13 red chameleons
15 green chameleons
17 blue chameleons
each time two different colored chameleons would meet, they would change their color to the third one. (i.e.. If green meets red, they both change their color to blue.) is it ever possible for all chameleons to become the same color? why or why not?"

Q8:
You have 12 coins. One of them is counterfeit. All the good coins weigh the same, while the counterfeit one weights either more or less than a good coin. Your task is to find the counterfeit coin using a balance-scale in 3 weighs. Moreover, you want to say whether the coin weighs more or less. (have patience b’coz its solvable)

Q9:
There are 10 ball producing machines out of which 9 machines produces 10gm balls and the remaining one produces 11gm balls, you are given with a weighing balance with all kinds of weights so that u can measure any weight you like, you have to identify which machine produces the 11gm balls but you can weigh only once. You have sufficient number of balls from each machine.

Q10:
you have $10,000 dollars to place a double-or-nothing bet on India in the Pepsi cup (max 7 games, series is over once a team wins 4 games). Unfortunately, you can only bet on each individual game, not the series as a whole. How much should you bet on each game, so that, if the yanks win the whole series, you expect to get 20k, and if they lose, you expect 0? Basically, you know that there may be between 4 and 7 games, and you need to decide on a strategy so that whenever the series is over, your final outcome is the same as an overall double-or-nothing bet on the series.