Which is more important Queestion or Answer ?

A passage taken from a speech made by Emrehan Halici

Let me begin with "questions"... or even better "questions and answers". These two are certainly related notions. You are provacated by questions to go into a passionate search for an answer. They are in no sense separate. Yet, if you ask which is the most important, questions or answers, our vote would directly be on the side of the former option without any hesitation. A question is like a challenge or even a seductive claim, of which it is hardly possible to stay indifferent to. An answer, quite the opposite, is a defence strategy that attempts to protect your unity in a passive way. You remain passive even when you are ready to take this duel against the question: An answer removes the sense of freedom and all the vividness that a question might potentially possess.

Then, what is it that is so important in an answer? The importance of an answer lies in this passionate search itself, one that is mostly about the experience of "looking for" rather than simply finding what it might be. Passion is there as long as you keep searching. It is over, once the answer is found.

Moreover, the answer that you have found may not always keep its soundness as it once appeared at the beginning. An answer to a particular question can loose its strength depending on location and time as well as on scientific-technological developments.

Put in an analogous way, a question is much like a wide-dimensional universe suggesting full diversity, whereas an answer is simply a target point that is being focussed upon. The endless number of question marks creates this mysterious universe. Yet despite the whole attraction of this so-called mystery, we are at times required not only to provide straight forward answers but to also provide solutions.

I mentioned earlier how an answer removes the sense of freedom a question suggests. Solutions have a much stronger effect. They completely erase the question from the surface and consequently establish an end to it.

An answer and solution is the final destination for questions. At most times, passengers do not pause at other stops, and instead jump to this final destination without making the most out of their journey. However, those who enjoy the adventure that is found along the deep corridors of their brain do not have the intention of setting out on a journey where the final desination is clearly visible to them. And they are simply right.

In fact, it is no more than these adventurous dreams and fantasies that lie behind the developments and successes in those subjects such as science, technology and art.

Emrehan HALICI

PIGEONHOLE PRINCIPLE

 

The pigeonhole principle is one of the simple-minded ideas imaginable, and yet its generalization involves some of the most profound and difficult results in all of combinatorial theory.

Pigeonhole Principle: if there are more pigeons than pigeonholes, then some pigeonhole must contain two or more pigeons. More generally, if there is k times more pigeons than the holes, then some pigeonhole must contain at least k+1 pigeons.

Puzzle 1:

There are 15 computers and 10 printers in the office, in every 5minutes a subset of computer asks for printers. How many different connections are necessary between computers and printers to guarantee that if 10 (or fewer) computers ask for a printer, there will always be connections to permit each of these computers to use a different printer?

Answer:

Very practical and interesting Problem, I liked it a lot because it kept me busy for an hour, also when I went for insight of it, I found some interesting constraints which I will share. If you haven’t found the answer yet, I will suggest you to look into the puzzle keeping the above principle in mind and try to find out what is the minimum number of connections that should be there in order to satisfy the principle without getting into the how exactly the connections will be made. Once you get that number, I can bet it will take few minutes to find the exact connections.

There need to be 60 connections at least by pigeonhole principle. If it’s less than 60 then some printers will have 5 or less connections, so if all the 5 of the computers have not asked for a printer then that printer will not be used. Hence we need at least 6 connections per printer. So the now the problem boils down to can we make 60 connections to achieve the desired result. There are many solutions possible, following is mine

Printer	A	B	C	D	E	F	G	H	I	J
Computer	1 2 3 4 5 6	2 3 4 5 6 7	3 4 5 6 7 8	4 5 6 7 8 9	5 6 7 8 9 10	6 7 8 9 10 11	7 8 9 10 11 12	8 9 10 11 12 13	9 10 11 12 13 14	10 11 12 13 14 15

 

Aclose look at the table, will reveal that the boundary computers like computers number 1 and 15 have just 1 connections and the number of connections keep on increasing for computer numbers towards the center like computer numbered 6, 7, 8, 9 and 10. We can make a different arrangement where each one has same number of connections. But I prefer this one because in reality the usage of resource varies from person to person, so then we can profile them, and less usage guy can be towards the border and the more usage guy can be towards the center. Also we can do some randomization for using all the printers equally during low load conditions.

It’s so funny how our mind works, with a constraint (the minimum number) and with a definitive goal it works better. The moment we gave it an approximate number it found out how to do the connection. It also shows how our brain utilizes the symmetrical patterns.

In real life it helps if you can set some definitive goals.

 

Some more puzzles if you try to find the diversification of this principle

1.      How large a set of distinct numbers between 1 and n is needed to assure that the set contains a subset of five equally spaced numbers a1,a2,a3,a4,a5 such that

a2-a1=a3-a2=a4-a3=a5-a4 ?

2.      Prove that in a group of 6 people, there is always a subset of 3 people who either know each other or don’t know each other. (very interesting)

Out of Box Thinking !

OBT(Out of Box Thinking) can be the best complement to a puzzle solver. It's a very widely used word to show the extraordinary brilliance of some guy. But this parameter has no scale, you can't say this solution is more OBT than that one. It's just a feeling that comes from inside of the observer or listener. You can never measure or define the OBT clearly but you will identify immediately as soon as it happens. I never get impressed by ordinary things, or just above average things, but this OBT impresses me the most. I love seeing people who has radical thinking and they come up with OBT very often. Talking to them is always a pleasure.


I will love to share some of the Out of thinking i came across in my life and i want you people to share your own experiences.


Puzzle:

There's a tennis tournament with one hundred twenty seven players, Shockley began, in measured tones. You've got one hundred twenty-six people paired off in sixty-three matches, plus one unpaired player as a bye. In the next round, there are sixty-four players and thirty-two matches. How many matches, total, does it take to determine a winner?


OBT :

126
It takes one match to eliminate one player. One hundred twenty-six players have to be eliminated to leave one winner. Therefore, there have to be 126 matches.


Ref : HowWould You Move Mount Fuji?


Don't forget to share your experience !

Logic Challenge !

There was a good job going in the office and the boss could not decide which of the three candidates should have it, each of them being worthy of it and all of them very bright indeed. So he set them a problem and the one who solved it would get the job. He showed them five discs, three black and two white and said: I am going to put a disc on the forehead of each of you. You will be able to see the others discs but not your own. There will be no talking. By pure deduction you will have to work out what colour disc you have, and the one who does so gets the job.? He withheld the two white discs and put a black one on each of them. After a time one of the men stepped forward and successfully claimed the job. How did he figure out that he had a black disc on?


Come up with your Logic then We will Discuss !

Some Tricky Puzzles

1.Boston United's latest player lives on the 13th floor of a tower block. Every morning he takes the lift down to the ground floor and leaves the building. When he returns home in the evening, if there is someone else in the lift or it's raining he goes straight back to his floor directly. However, if there is nobody else in the lift or it hasn't rained he goes up to the 10th floor and walks up the remaining three flights of stairs. He hates walking up stairs so why does he do it?

2.There are 2 identical strings. If you light one of the strings at its end, it will take exactly one hour for it to finish burning completely. The string will not burn evenly - it is thicker in some places, thinner in others. For example, the string may not be half consumed exactly 30 minutes from lighting it at one end. You have no other means of telling time, and you want to know when exactly 45 minutes have passed. All that you have is a lighter and these 2 identical strings. What is the most accurate method you can use, given these conditions?

3.A water lily growing in a circular pond doubles in size every day. It takes thirty days to cover the whole pond. How long does it take to cover half the pond? 


Triumph 1: The person is dwarf and he can reach up to the 10th floor button in the lift and in rainy days he has an umbrella to use to press the 13th floor button. and while coming down he just has to press ground floor button, which he can reach easily.


Triumph 2: You have to realize the fact that how uneven the rope can be but if you light the rope from both sides it will take half an hour to complete burn. If you are agree with me then you got the answer.
Light one rope from both sides and the other from only one side, when the first rope burnt completely it's 30mins, and the 2nd rope would have taken 30 more mins to burn completely so light the other end of the second rope, so it will get finished in next 15mins.


Triumph 3: 29 days (You can impress your girl friend with this one, but don't forget to say sorry after you finished laughing)

Puzzles for School Children

Q1: Each child in a family has at least 5 brothers and 4 sisters. What is the smallest number of children the family might have?

Q2: Louise runs the first half of a race at 5 miles per hour. Then she picks up her pace and runs the last half of the race at 10 miles per hour. What is her average speed on the course?

Q3:what is ?
8
2 5 2
1 2 4 2 1
1 2 1 3 1 2 1
1 2 1 1 ? 1 1 2 1

Q4: How Many Days?Froggie fell down a 10-foot well. He cannot hop out. He has to climb out. He climbs three feet a day, but during the night, while resting, he slips back two feet. At this rate, how many days will it take Froggie to climb out of the well?

Q5: How Many Marbles?
Marta distributed 100 marbles among five bags.
Bag #1 and Bag #2 together contain 52 marbles.Bag #2 and Bag #3 together contain 43 marbles.Bag #3 and Bag #4 together contain 34 marbles.Bag #4 and Bag #5 together contain 30 marbles. How many marbles are there in each bag?

Q6: How Many Students?
A new school has opened with fewer than 500 students. One-third of the students is a whole number. So are one-fourth, one-fifth, and one-seventh of the students. How many students go to this school?

Q7: Pick a Pair
Ben has socks in five different colors: two pairs of blue socks, two pairs of black, three pairs of brown, four pairs of green, and four pairs of white. Ben, who is not very neat, doesn't bother to pair up his socks when he puts them away. He just throws them in the drawer. Now Ben is packing to go away for the weekend, but there's been a power failure and he can't see the socks in his drawer.
How many socks does he have to take out of his drawer to be sure he has at least two that will make a pair?

Q8: Sale!
An online shopping site reduced the price of one computer model by 25 percent for a sale. By what percentage of the sales price must it be increased to put the computer model back at its original price?

Q9: Which Way?
Once a boy was walking down the road, and came to a place where the road divided in two, each separate road forking off in a different direction.
A girl was standing at the fork in the road. The boy knew that one road led to Lieville, a town where everyone always lied, and the other led to Trueville, a town where everyone always told the truth. He also knew that the girl came from one of those towns, but he didn't know which one.
Can you think of a question the boy could ask the girl to find out the way to Trueville?


Post Your Solutions. I will Get back to you.

10 Common Interview 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 (Seat No 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.


Please post your Solutions. Also you can ask for solutions