Solution of 100 door puzzle....microsoft interview puzzle

Solution:

This problem is designed to seem overwhelming. You don’t have time to draw a diagram of 100 lockers and count 100 passes through them. Even if you did, solving the problem that way wouldn’t illustrate any skill or intuition, so there must be some trick that can be used to determine how many doors will be open. You just have to figure out what that trick is.

It’s unlikely that you’re going to be able to intuit the solution to this problem by just staring at it. What can you do? Although it’s not practical to solve the entire problem by brute force, solving a few lockers in this manner is reasonable. Perhaps you’ll notice some patterns you can apply to the larger problem.
Start by choosing an arbitrary locker, 12, and determining whether it will end open or closed. On which passes will you toggle locker 12? Obviously on the first pass, when you toggle every locker, and on the twelfth pass when you start with 12. You don’t need to consider any pass after 12 because those will all start farther down the hall. This leaves passes 2 through 11. You can count these out: 2, 4, 6, 8, 10, 12 (you toggle on pass 2); 3, 6, 9, 12 (on 3); 4, 8, 12 (on 4); 5, 10, 15 (not on 5); 6, 12 (on 6); 7, 14 (not on 7), and so on. Somewhere in the middle of this process, you will probably notice that you toggle locker 12 only when the number of the pass you’re on is a factor of 12. If you think about this, it makes sense: When counting by n, you hit 12 only when some integer number of n’s add to 12, which is another way of saying that n is a factor of 12. Though it seems simple in retrospect, this probably wasn’t obvious before you worked out an example.

Solution of 2 Egg Problem: Google Interview Puzzle

Solution:

Drop the first egg from 50.If it breaks you can try the same approach for a 50-storey building (1 to 49) and try it from 25th floor. If it did not break try at 75th floor. And use linear search with the remaining portion of storey we need to test. For example if the first egg breaks at 50 we need to try all possibilities from 1 to 49.

Now this looks a feasible solution. In computer student's jargon do a binary search with first egg and linear search with the second one. Best case is log (100) and worst is 50.

Move block in matrix

Question:
Given a m*n matrix and a person is sitting in (0,0) box, and he has to go to the (m-1,n-1) box of the matrix .And the person can only go to right or down box from its current box position . We need to find out the number of ways he can reach from start to destination box .

100 prisoner`s hat problem..

Question:
There are 100 prisoners , and a officer of them . Now the officer gave the command to the prisoner that next day they will be going to wear a hat which they will not be know its colour . But its colour will be either Red or Blue . And he says that all the prisoner will be standing in a line .
And then the officer will start asking the color of the prisoner one by one from the back . whichever prisoner says the wrong color of his hat ,gets shoot .So now we have to find out wat strategy should the prisoners should apply to safe maximum prisoners .

100 door puzzle....microsoft interview puzzle

Question:
Lets say you have a room with 100 doors in it. Initially, all of these doors are open. You have 100 people that will be entering the room. The 1st person toggles every door, 2nd person toggles every other door, 3rd toggles every 3rd door, ... , nth person toggles every nth door. How would you determine the state of all 100 doors after all 100 people have entered the room?

Find top 5 horse from 25 horses

Question:

how to find top 5 horses from 25 if there are only 5 lanes.In min no. of races?

Red Marbles and Blue Marbles puzzle...goggle puzzle

Problem:

you have two jars, 50 red marbles, 50 blue marbles. you need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. (when picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar) you can arrange the marbles however you like, but each marble must be in a jar.

8 ball puzzle select heavier from them....

Question:

You have eight balls all of the same size. 6 of them weigh the same, and two of them weighs slightly more. How can you find the balls that is heavier by using a balance and do this in minimum number of steps?

8 ball puzzle..to select lighter ball from them

Question:
Just Example : "Given 8 cue balls , one is weighing lesser than other 7. Find that(light weight) ball using just 2 chances on balance weight."

How to find a general solution to these kind of question? How to divide this set of balls? Is there any finer method or general formula?

Coins on the Table : Microsoft Puzzle

This is not one of the classic Microsoft puzzle. I recently heard from a friend. I am listing the problem below.
Question:
There is a table on which a number of coins are placed. You also know that there are as many coins with Head up as many coins with Tail up. Now you have to divide the coins (number of coins is even)
into two equal piles such that number of coins with Heads up and Tails up in either piles be the same. The catch is you are blind folded and you cannot determine the sides (for sure) if you are blinded

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Shopkeeper Problem with Solution

Problem 1: One Side Only (Simple)

This is simply the numbers 2^0,2^1,2^2 ….. that is 1,2,4,8,16 ……….
So for making 1000 kg we need up to
1, 2, 4, 8, 16, 32, 64, 128, 512.

Problem 2: Both Sides (Medium)

For this answer is 3^0,3^1,3^2 …. That is 1,3,9,27,81,243,729

Problem 3: Incremental (Hard)

This is exactly a problem solved by Gray code.
Gray codes are named after the Frank Gray who patented their use for shaft encoders in 1953
A Gray code represents each number in the sequence of integers {0...2^N-1} as a binary string of length N in an order such that adjacent integers have Gray code representations that differ in only one bit position. Marching through the integer sequence therefore requires flipping just one bit at a time.

Example (N=3): The binary coding of {0...7} is {000, 001, 010, 011,
100, 101, 110, 111}, while one Gray coding is {000, 001, 011, 010,
110, 111, 101, 100}.

13 Balls problem : One of Hardest Interview Questions

One of the most classic puzzles involving balls is figuring out the odd one out using common balance.There are many levels of puzzles based on the same concept for different levels of interviews - Simple ones for phone interviews to the most gruelling 1 hour hard work needing hard ones.

Problem space
The general problem is you will be given n balls and one of them is either heavier or lighter and you are asked to find out the minimum number of weighings using a common balance required to find out the odd one out.

Example 1:8 Balls,Odd ball being heavier
This is the simplest question among the lot and is often used during phone screenings.The question is to find out the minimum number of weighings required to spot the odd heavier ball among 8 identically looking balls using a common balance.Answer is 2 and the solution is given in the next paragraph.

25 Horses Puzzle

Question:
Given 25 horses, find the best 3 horses with minimum number of races. Each race can have only 5 horses. You don't have a timer.
Now the challenge is how we can do it in 7 races.

Polar Bear : Microsoft Interview Question

Question:
One of the most asked and well known microsoft interview question is that of the walking bear.The question is still asked because a lot of people have either not heard of it or most of them don't know the correct solution yet.

If a bear walks one mile south, turns left and walks one mile to the east and then turns left again and walks one mile north and arrives at its original position, what is the color of the bear.

3 Classic Weighing puzzles :Simple Medium and Hard (Google puzzle)

In this post I want to describe about a series of puzzles called weighing puzzles. These puzzle vary in hardness from simple to extremely mathematical involving either expertise in some fields or extreme ingenuity. Either you know it or you figure out it using extreme intelligence. So here is the chance for some people to burn your grey cells.

I am putting forward three puzzles with varying range of hardness. Sometimes you may feel the hardest one is very easy for you have already come across the theory, but I still made it the hardest for the people who will be solving it with out knowing the theory behind it, giving them an option to figure out a small part in evolution of computational history.
There is a shopkeeper who wants to weigh things who has a common balance. He must be in a position to weigh things of all possible integral weighing units from 1 to a given maximum sum. The question will be either about how many weights you will need or how will you weigh.

2 Egg Problem: Google Interview Puzzle

My intention here is not to trouble Google interviewers. I was just collecting some classic puzzles and found this one and a small Google search showed me that this is a Google interview puzzle to my pleasant surprise. But many of the answers I found were either wrong or totally twisted. I am making no surety of the answer I give and I am open to your remarks or suggestion or corrections.


Question:

The Standard Problem in simple writing goes like this:

* You are given 2 eggs.
* You have access to a 100-storey building.
* Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100 th floor.Both eggs are identical.
* You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
* Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

4 dogs chasing on corners of square

Puzzle:
There are four dogs, each at the counter of a large square. Each of the dogs begins chasing the dog 
clockwise from it. All of the dogs run at the same speed. All continously adjust their direction so that 
they are always heading straight towards their clockwise neighbor. How long does it take for the dogs to 
catch each other? Where does this happen? (Hint: Dog’s are moving in a symmetrical fashion, not along the edges of the square).

Tansporting 3000 banana riddle.(microsoft puzzle)

Puzzle

A banana plantation is located next to a desert. The plantation owner has 3000 bananas that he wants to transport to the market by camel, across a 1000 kilometer stretch of desert. The owner has only one camel, which carries a maximum of 1000 bananas at any moment in time, and eats one banana every kilometre it travels. What is the largest number of bananas that can be delivered at the market?

Enclosing land by fence pieces.(Microsoft puzzle)

Puzzle
You are given one 44-meter piece of fence and 48 one-meter pieces of fence.  Assume each piece is a straight and unbendable.  What is the large area of (flat) land that you can enclose using these fence pieces?

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Picking larger of two cards from 13 cards.(microsoft riddle)

Puzzle:
Someone picks two cards from a deck of cards. The cards have one is higher than the other. (In other words, the person picks two distinct numbers in the inclusive range 1 through 13.)  The cards are placed face down on table in front of you.  You get to choose one of the cards and turn it face up.  Now, you will select one of the 2 cards (one of whose face you can see, the other one you can't).  If you select the highest card, you win.  Design a card-selection strategy for which your chance of winning is strictly greater than 50%.

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