1. In a plane, n points are given i.e. the input is (x1,y1), (x2,y2)... (xn,yn). Now given these n points.Find the maximum number of collinear points.

Answer :

The duality algorithm would work. Find the point of intersection with maximum no of lines incident on it in the dual plane. It works in O(n^2).

2. You are given biased coin. Find unbiased decision out of it?

Answer :

Throw the biased coin twice.Classify it as true for HT and false for TH. Both of these occur with probability=p*(1-p),hence unbiased. Ignore the other 2 events namely HH and TT.

3. You are shrunk to the height of a nickel and your mass is proportionally reduced so as to maintain your original density. You are then thrown into an empty glass blender. The blades will start moving in 60 seconds. What do you do?

Answer :

You simply jump out. As you are scaled down, the ratio of muscle mass to total mass remains the same. Potential energy is given by E = mgh. So, if E/m is unchanged (where E is the energy expended in expanding your leg muscles, and m is your mass), then h is unchanged. Mini-me jumps as high as me. This is the reason why grass-hoppers can jump about as high as people.

4. There are 8 identical balls. One of them is defective. It could be either heavier of lighter. Given a common balance how do you find the defective ball in least number of weighings.

Answer :

Weigh 3 balls against 3 others.

Case A :

If, on the first weighing, the balls balance, then the defective is among the 2 remaining balls and can be determined using 2 weighings making it a total of 3.

Case B :

Step1: If, on the first weighing, the balls don't balance.
If the balls do not balance on the first weighing, we know that the odd ball is one of the 6 balls that was weighed. We also know that the group of 2 unweighed balls are normal, and that one of the sides, let's say Side A, is heavier than the other (although we don't know whether the odd ball is heavy or light).

Step 2 : Take 2 balls from the unweighed group and use them to replace 2 balls on Side A (the heavy side). Take the 2 balls from Side A and use them to replace 2 balls on Side B (which are removed from the scale).

I. If the scale balances, we know that one of the 2 balls removed from the scale was the odd one. In this case, we know that the ball is also light. We can proceed with the third weighing amd determine the lighter of the 2 balls ,hance the defective.

II. If the scale tilts to the other side, so that Side B is now the heavy side, we know that one of the three balls moved from Side A to Side B is the odd ball, and that it is heavy. We proceed with the third weighing and determine the heavier one ,the defective.

III. If the scale remains the same, we know that one of the two balls on the scale that was not shifted in our second weighing is the odd ball. We also know that the unmoved ball from Side A is heavier than the unmoved ball on Side B (though we don't know whether the odd ball is heavy or light).

Step 3 (for Case B) : Weigh the ball from Side A against a normal ball. If the scale balances, the ball from Side B is the odd one, and is light. If the scale does not balance, the ball from Side A is the odd one, and is heavy.

5. You have given an array from 1 to N and numbers also from 1 to N. But more than one number is missing and some numbers have repeated more than once. Find the algo with running time O(n).

Answer :

All the numbers are positive to start with.Now, For each A[i], Check the sign of A[A[i]]. Make A[A[i]] negative if it's positive. Report a repetition if it's negative.Finally all those entries i,for which A[i] is negative are present and those i for which A[i] is positive are absent.

6. How much should you charge to wash all the windows in Seattle?

Answer :

As crazy as it might sound, questions like these demonstrate your ability to think through a complex problem with little or no information. They expect you to take an educated guess. Most of the time you can ask them questions like - how many buildings are there in Seattle.

7. If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

Answer :

7.5 degrees (the hour hand is 1/4th of the way between 3 and 4, the angle measure of that is 360/12 = 30 degrees between hours / 4 = 7.5 degrees)

8. How many piano tuners are there in the entire world?

Answer :

1) At first list out all the piano manufacturing companies in the world.

2) Then look into their purchase records and find out the piano purchasers information.

3) (a) If the purchase is made by an individual or a house hold then the piano is played at best case by all the people of the house.

(b) Else if the piano is purchased for school then list out the students that opted the piano course in their music curriculum.

(c) If the piano is purchased by a Church then count the no of major or minor events of the church and count the piano users.

Sum up all the numbers to get more or less accurate piano users count.

9. Classic Egg Puzzle Problem You are given 2 eggs.You have access to a 100-store 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-store 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.

Answer :

Let "d" be the number of drops required to find out the max floor.we need to get the value of d.

let's say if we drop from height d then if it breaks then we have d-1 floors to check for the second egg . so max of "d" drops, so first we will drop it from height "d" if it doesn't break at a height "d" then we are left with "d-1" drops,so lets drop it from d + 'd-2' + 1 height suppose if it break there then you are left with 'd-2' drops.
and so on until that sum is less than 100, it's like a linear search,

in equations,

(1+(d-1))+ (1+(d-2)) + .... >= 100

here we need to find out d

from the above equation

d(d + 1)/2 >= 100

from above d is 14

10. You are at a party with a friend and 10 people are present including you and the friend. your friend makes you a wager that for every person you find that has the same birthday as you, you get $1; for every person he finds that does not have the same birthday as you, he gets $2. would you accept the wager?

Answer : No