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### Google Interview Questions Part - 2

Google Interview   Questions Part - 2

answer to boy and country question:
say there are 100 families, that means there will be exactly 100 boys.     Lets figure out how many girls.
50 families will have a girl on their first try,
25 will have a girl on their second try
12.5 on third and so on.
so 1/2 of the population has at least 1 girl, 1/4 has at least 2 and so     on.
this reduces to avg # of girls per family = 1/2 + 1/4 + 1/8? = 1
so the proportion is 1 to 1

FWIW I interviewed there 11 times and didn?t get asked any of these.     Indeed, nothing like these. These are just puzzles. The questions I got     asked were arguably harder, but certainly more directly related to     engineering and computer science.

Query:     How do you cut a rectangular cake into two equal pieces when someone has     already taken a rectangular piece from it? The removed piece an be any size     or at any place in the cake. You are only allowed one straight cut.Soln. Proposed:
Cake is a three dimentional thing. Irrespective of the size of a rectangular     piece cut from it, if we cut the cake horizontally from the middle of its     height, it?ll be cut in two equal halves.

the answer to the clock question is actually 23
the first round starts at midnight when both hands are on 12 overlapping,     then an overlap occurs after each hour before noon, so, this is 11 overlaps,     + 1 at noon, + 11 more on the second round, making it 23 overlaps per day,     and the 24th one will be actually the first overlap of the next day,done

Cake:
Start from a easy one. A straight line passing through the center of a     rectangle will cut the rectangle into two halves with same area.
Now the problem. A line passing through both center will cut the cake into     tow halves with same area.
Car:
qbaler is correct I think. but i can not find what?s wrong with following     calculation.
If the possibility of seeing 1 car in 10 min is p, then:
1) chance of seeing 1 car in the first 10 min = p*(1-p)^2
2) .. = (1-p)*p*(1-p)
3)so, the chance of seeing 1 car in 30 min is:
3*p*(1-p)^2 = 0.95
=> p = 1.465

guys
the answer to the car question is
cuberoot 95/ cuberoot 100
imagine that you roll a dice. what is the possibility to have a 1? 1/6 right
roll it twice.. it s 1/36
so think that 30 minutes is three times 10 minutes.
to 95/100 (95%) is a cube of three numbers.
which gives the correct result as cuberoot 95/ cuberoot 100

The probability to have a 1 show up if you roll a 6 sided die is indeed     1/6. You could end up with (1), (2), (3), (4), (5), or (6), and only (1) is     a favorable outcome.
With two dice, there are 36 possible outcomes. I won?t list them all,     but here are a few:
(1,1), (1,2), (1,3), ?
(2,1), (2,2), ?
(3,1), ?
There are several favorable outcomes where a 1 is present out of the 36     rolls. There are 6 ways for the first die to be any number while the second     die is a 1, and there are 6 ways for the second die to be any number while     the second die is 1. Having counted (1,1) twice, you end up with 11/36 as     the probability of having at least one 1 show up when you roll two dice.
Unless you are asking for (1,1), then the probability is 1/36.

puttyshell:
The question doesn?t ask ?What is the probability of seeing 1 car in 10     minutes, and no cars in the other 20 minutes??
Also, your final answer of p = 1.465 is not possible because that value     is greater than 1!

For the Mike and Todd problem, it says there is a tricky question. I got     a different angle of the problem.
Let T have x, then M has x+20.
They both have to give sth so they have 21 between them.
So x should be 1, so that M gives 20 and T gives 1 to make 21 between     them.

For the boy girl ratio problem, the number of girls is a taylors series:
probability of having a boy in the first try is 0.5
and the second is 0.25 etc. assuming no kids die then
the number of girls would follow:
x * (0.5 + 0.25 + 0.125 + ?) or Sum(1/(2^i), i=1..infinity) which is equal     to 2.
So on average there should be 1 boy to 2 girls.

for the cake problem?.      if the cut is made horizontally in the middle
of the depth of the cake it will be 2 equal pieces, no matter what the
size or shape or place of the cut?
And for the clock? answer is 22?this can be found easily , as each     overlap of the 2 hands occur at 12/11th of an hour?

For the searching the words in dictionary.. I feel the binary search as     the best method. As the search will be reduced to half after each iteration.

For the cake problem. As the original cake and removed piece are     rectangles. If you think these in 3dimensional view. Any line passing throug     their centroid( I mean center of gravity) will be the single straight cut.     If you cut in any other ways you can be proved false with some case.

qbaler,     you?re right that 1/2 + 1/4 + 1/8? = 1. however, the chance of having a     boy is still 1/2. So the proportion is 1 to 1/2 (or 2 to 1)

Assuming it?s an analogue clock, the clock is probably built with one     skrew in the middle which hold the two hands in place. Since it is most     always one skrew for both hands, the two hands overlap in the middle all day     and night. So the answer is that the hands overlap all day and night.

Regarding the clock angle prob:
Solution:-
We need to identify two things:
1. Angle movement per hour :- 360/12 = 30 degree
3. Angle movement per minute corresponding to per hour :- 0.5 (1 hour = 30     degree; 60 minute = 30 degree; 1 minute = 30/60 = 0.5 degree)
So, 15 minute movement will create angle of 7.5 degree (.5 * 15) between     hour and minute hand.

1. by colour
3. nothing queen doesnt live in the city and her husband was unfaithful
4. take 6 then take 2
5. find the man with the missing piece and get it
6. less then pianos
7. joy is to read this and know some questions so u can talk to yourself you     are not dump
8. $20 and$1
9. dont understand my english poor, dont know when they achieve their mit     and the sentence with 72
10. if its not 0 so its 360
11. 1&2 then 1 come back then 5&10 then 2 come back then 1&2
12. 0.95
13. girls > boys cause they want boys
14. hmm again my english poor dont understand the sentence

Maybe I am wrong, but I see people made the clock question over     complicated. The Way I see it is that for each hour the minute hand makes a     full circle, so for each hour they over lap only once and therefore for 12     hours its gonna be 12 times.

The boy girl problem is simple (once you get past the implicit assumption     that boys/girls are each born 50% of the time, which technically isn?t     exactly true).
No matter what strategy people use, every time someone gets pregnant,     there is a 50/50 chance of boy/girl. The final ratio is 1:1.
A better formed problem would be a room full of coin flippers. If     everyone flipped until they got a Head, in the end, you would expect a total     of 50% heads and 50% tails. Figure out a different answer, then take it to     Vegas and try to beat a roullette wheel :)

Actually the ?8 ball? question is much more interesting when we do     not know that odd ball is lighter or heavier others. We will need one more     weighing though, but we can increase number of balls to 12.

ques: You have to get from point A to point B. You don?t know if you     can get there. What would you do?

Ans: I will start searching for Point B moving on a spiral path starting     from point B.

ques:      Imagine you have a closet full of shirts. It?s very hard to find a     shirt. So what can you do to organize your shirts for easy retrieval?

Ans. separate shirts on the basis of color and then arrange according to     company?s name in alphabetical order.

2. Imagine you have a closet full of shirts. It?s very hard to find a     shirt. So what can you do to organize your shirts for easy retrieval?
I would first ask myself what criteria I normally use when looking for a     shirt. I would then sort sort them according to those criteria, pretty much     like a DBA does when indexing tables to optimize them most frequent queries.

Dingo, you are right. I was actually thinking the flawed way, until I     tried to right a Python script to simulate the problem (I?m a good     programmer, but terrible at calculus). You don?t even have to run to see     that the result will always be 0.5 (assuming random() is really random :)
import random
boysCount = 0
girlsCount = 0
for a in xrange(10000000):
isGirl = random.random()
while isGirl

Q: You have an empty room, and a group of people waiting outside the     room. At each step, you may either get one person into the room, or get one     out. Can you make subsequent steps, so that every possible combination of     people is achieved exactly once?
A: Yes.
See if you notice the pattern (0 = outside, 1 = inside):
000000
000001
000011
000010
000110
000111
000101
000100
001100
001101
001111
001011
001001
001000
011000
011100
011110
011111
010111
010011
010001
010000
This pattern will cover every possible combination and can be repeated     for any number of bits (people). Other valid patterns may exist.

Q: You have to get from point A to point B. You don?t know if you can     get there. What would you do?
A:
I?d start by googling ?A B?, gathering as much information as     possible;
Then, I?d try to talk to someone in the team knowledgeable on those     points;
Next, I?d go back to my lead and make sure I?ve understood what A and B     are;
Hopefully, this should give me enough information start the journey;

Clock hands will overlap 22 times (All times approximate):
00:00, 01:05, 02:10, 03:15, 04:20, 05:25, 06:30, 07:35, 08:40, 09:45, 10:50,
12:00, 13:05, 14:10, 15:15, 16:20, 17:25, 18:30, 19:35, 20:40, 21:45, 22:50

Q: How many piano tuners are there in the entire world?
Assuming:
* World population 6 billion
* One in 10000 people own a piano
* One tuner will tune, on average, 2 pianos a day
* A piano needs tuning once every year
There are 600000 pianos;
They will require 600000 tuning every year
One single tuner can tune 520 pianos a year (2 tunes x 260 week days in the     year)
Approximately 1153 piano tuners are required.
In questions like this, they are not really interested in the answer you     give, but how did you get to it. Stating your assumptions as clearly as     possible helps. Also, you may want to get to your answer using two or     rationales. In this case, you may want to guess the number of pianos by the     number of house holds in the world and the ratio of those with enough money     to own a piano, etc.

Clock hands - 24 times per day. For those of you who stated that at the     end of the day (midnight), it is actually the next day - if you use this     assumption, then you must count that as the first time they cross on that     day. You can simplify the question by asking ?How many revolutions does     the minute hand make in a day?? 24
Unfaithful husband - the only woman who isn?t aware of the infidelity     immediatelly kills her husband (everyone else already knows he did it,     including the Queen - how much more proof do you need?).

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!)
360/(12*4)= 7.5 degree is the angle ?where 4 comes from (60/15)

The cake: It?s not possible, in practical terms, to cut any cake     equally. Cutting it horizontally ignores the roundness at the top of the     cake, to say nothing of the extra frosting on top, or who gets the rose     decoration. Even if one rules those things out, there will always be     something to quarrel about, no matter how the cake is divided. That?s why     in a case like this, you ask one recipient to cut it, and the other     recipient to have first choice re which piece he wants. Trust me, I have     twin boys.

Two MIT math graduates bump into each other. They hadn?t seen each     other in over 20 years.
The first grad says to the second: ?how have you been??
Second: ?Great! I got married and I have three daughters now?
First: ?Really? how old are they??
Second: ?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..?
First: ?Right, ok.. oh wait.. I still don?t know?
second: ?Oh sorry, the oldest one just started to play the piano?
First: ?Wonderful! my oldest is the same age!? Problem: How old are the     daughters?