Aeroplane..(Microsoft puzzle)

Riddle:
The puzzle question is : On Bagshot Island, there is an airport. The airport is the homebase of an unlimited number of identical airplanes. Each airplane has a fuel capacity to allow it to fly exactly 1/2 way around the world, along a great circle. The planes have the ability to refuel in flight without loss of speed or spillage of fuel. Though the fuel is unlimited, the island is the only source of fuel.

What is the fewest number of aircraft necessary to get one plane all the way around the world assuming that all of the aircraft must return safely to the airport? How did you get to your answer?

Notes:

(a) Each airplane must depart and return to the same airport, and that is the only airport they can land and refuel on ground.

(b) Each airplane must have enough fuel to return to airport.

(c) The time and fuel consumption of refueling can be ignored. (so we can also assume that one airplane can refuel more than one airplanes in air at the same time.)

(d) The amount of fuel airplanes carrying can be zero as long as the other airplane is refueling these airplanes. What is the fewest number of airplanes and number of tanks of fuel needed to accomplish this work? (we only need airplane to go around the world)

Rectangle 8 part puzzle

Question:

We have a rectangle
It is divided in eight parts by three vertical and one horizontal line so that there are 8 chambers.
Now we have numbers from 1-8 to be filled in these chambers.
Rule : No two consecutive numbers must be present either side to side or diagonal
Invalid situation example
Given 5 at position 2 then 4 cannot occur at any of the give position.

Minimum no. of rats needed for finding poison in bottle....google puzzle

Question:
There are 8 bottles, one has poison. What's the minimum number of rats you need to find the poison bottle in time T, and how? (You get the rats you need all at once, feed them all at the same time, and poison kills them after time T.)


Solution:

representation in binary numbers
1-0001
2-0010
3-0011
4-0100

prove that n(n2-1) is div by 24...amazon puzzle

Question:

prove that n(n2-1) is div by 24

Note: n is odd and >=3

Solution:

N(N^2-1)=(N-1)N(N+1)
means it must be divisible by 2 and 3

since 24=2X2X2X3

Solution:Weight difference puzzle....morgan stanley logical puzzle

Solution:

I believe the solution is as follows (assume initial configuration to be an empty bucket at the top and a bucket with the stone in it at the bottom):

1. Prince goes down, rock goes up.
2. Queen goes down, Prince goes up.
3. (the rock is dropped from the top of the tower)

Weight difference puzzle....morgan stanley logical puzzle

Question:
There are 3 people on a tower which may collapse due to fire. King(78 kg),Queen(42kg) and Prince(36kg).There is a pulley on the tower with baskets tied to it on both the sides of rope around the pulley. There is a 30kg stone in one of the baskets. 

There can be two persons or a person and a stone or a person or a stone in the baskets keeping in mind that the weight difference is not more than 6kg else rope would break. You have to bring all the three on ground safely

Probability of rolling a 10 and an 11 before rolling a 7?

Question:
What is the probability of rolling a 10 and an 11 before rolling a 7?

Solution:
As stated, must roll a 10 and 11 before rolling a 7

P(10)=3/36 P(11)=2/36 P(7)= 6/36
Two options: a) 10 first or b) 11 first
a) P that 10 is rolled before 7 is rolled:
P(10)/P(7)= 3/6
then 11 rolled before 7 is rolled:
P(11)/P(7)= 2/6

Solution: Toggling of 100 switches..

Solution:

This is a little tricky. Say switches nos are 1 to 100.
Here
after 1st round, all switches are ON (All were OFF, so toggling will make all ON)
after 2nd round, all switches divisible by 2 (switch no divisible by 2) are TOGGLED
after 3rd round, all switches divisible by 3 (switch no divisible by 3) are TOGGLED
after 4th round, all switches divisible by 4 (switch no divisible by 4) are TOGGLED
.......

Toggling of 100 switches..

Question:
Suppose there are 100 lights, which are all off. First round past them, turn all on;
Second round past, turn every other off;
Third round, turn every third on;
vice verse;
Ask the 100 round past, which light will be on?

Probability of rolling a 10 and an 11 before rolling a 7

Question:
What is the probability of rolling a 10 and an 11 before rolling a 7?

Solution: Maximum no. of matches puzzle

Solution:
56 points are distributed to 8 team. In the worst case, team0 loses all the games, he gets 0 point. team1 win two games with team0 and loses all other games, he gets 2 points.
In the same way, team2 gets 4 points, team3 gets 6 points. So there are 44 points left which can be distributed to the remaining 4 teams. So the assurance points for a team should be 11 points.

Maximum no. of matches puzzle

Question:
Consider a series in which 8 teams are participating. each team plays twice with all other teams. 4 of them will go to the semi final.How many matches should a team win, so that it will ensure that it will go to semi finals.?

Minimum no. of queens in chess board

Question:
Imagine there are infinite number of Queens (Chess Game Piece) with u. Find the minimum number of queens required so that every square grid on the chess board is under the attack of a queen. Arrange this minimum no. of Queens on a chess board.

Solution:Amazon puzzle: find probability of men to go in room

Solution:

1 - 1/2 * 1/2 * 1/2 * 1/2 =>  15/16

explanation:

It is the combined probability of all possible events minus the probability that all four people will NOT open the door (1/2)^4. Another way to look at this problem would be to take the sum of the probabilities of all possible ways that the door will be opened:

Amazon puzzle: find probability of men to go in room

Question:
There are 4 people in a closed room and you are waiting outside to enter into the room. You can enter only when one of them opens the door. The probability that somebody will open the door is 1/2. Now what is the probability that the door will be opened so that you can go inside?

Solution:Find average salary without knowing other`s salary

Solution:

Lets name these employees A, B, C and D

1. A chooses any random value and whispers it to B privately
2. B chooses any random value and whispers it to C privately
3. C chooses any random value and whispers it to D privately
4. D chooses any random value and whispers to to A privately

Find average salary without knowing other`s salary

Question:
How can four employees calculate the average of their salaries without knowing other's salary?

Solution:Distance between 2 poles...amazon puzzle

Solution:
The distance between poles is zero. In this case, the cable will be hanging directly down and its center be 8mts down which is half of its length.
The height of the poles are 15mts, so 15mts - 8mts = 7mts.

POST YOUR OPINION IF YOU HAVE BETTER SOLUTION

Distance between 2 poles...amazon puzzle

Question:

There are two poles of equal height 15mts. One cable with length 16mts is hanging between that two poles. The height from center of the cable to earth is 7mts then what is the distance between that two poles.

Solution: Arrange numbers 1-8 in 2X4 matrix with no consecutive...Adobe puzzle

Solution:

1. keep no. in group of two alternate numbers.
{1,3} {2,4} {5,7} {6,8}

2.now fill the center 4 block with two group containing first and last number.
(1,3) {6,8}

- 1 8 -

- 3 6 -

3. now fill with other group.

5 1 8 4
7 3 6 2

Arrange numbers 1-8 in 2X4 matrix with no consecutive...Adobe puzzle

Question:
There is a 2X4 matrix, in this you are supposed to arrange the numbers from 1-8, so that no consecutive numbers are adjacent(vertically, horizontally and diagonally) to each other. It is possible to do if one keeps on trying it randomly
but it can be done with an intelligent approach too. What would that be?

Solution: Find no. of acute traingle from cube having 8 vertices

Solution:
Acute angled triangle can be formed by connecting the diagonal of three adjacent faces of the cube.
The number of ways three adjacent faces can be chosen is (6x4x2)/(3x2x1) = 8
So the total number of acute angled triangle is 8.

POST YOUR OPINION IF YOU HAVE BETTER SOLUTION

Find no. of acute traingle from cube having 8 vertices

Question:
Think of the 8 vertices of a given cube. You are allowed to join three
vertices to form a triangle. How many such unique acute triangles can you
make ??

Solution of 6 litre from 7 & 4 litre

Solution:
1. Fill 7 liter tumbler fully: 7 - 0
2. Fill 4 liter tumbler fully by pouring from the 7 liter one: 3 - 4
3. Empty the small one: 3 - 0

6 litre from 7 & 4 litre

Question:
There are two tumblers one 7 litre tumbler, one 4 litre tumber and ample water. Get 6 liters of water in 7 litre tumbler.