Google Interview Questions paper

Google interview questions

1. 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
2. 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.
3. 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.
4. 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
5. 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
6. guys
   the answer to the car question is
   cuberoot 95/ cuberoot 100
   the answer is easy.
   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
7. 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.
8. 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!
9. 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.
10. 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.
11. 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?
12. 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.
13. 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.
14. 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)
15. 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.
16. 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.
17. 1. by colour
    2. buy some dictionary first
    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
18. 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.
19. 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 :)
20. 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.
21.  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.
22.  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.
23. 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.
24. 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
25. 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.
26. 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;
27. 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
28. 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.
29. 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?).
30. 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)
31. 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.
32. 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?
    ? The answer: Unknown.
    The solution makes false assumptions:
    1.) The guy knew that two possible combinations had the sum 14
    2.) The guy could see the building number
    3.) Two children cannot be the same age.
    Key #3 is the most important. It is possible to have two six year olds and a two year old. Twins. With twins, there is ALWAYS an older child. So, it is perfectly legit to say that you have two six year olds, one two year old, and the oldest began playing piano.
33. Jay Jay? What about 11:55 and 23:55?
    Cake? Horizontal cut answers assume the rectangle removed is the same height as the cake.
    As pointed out by Jay Jay, if I asked you any questions like these it is your thinking process that I care about. Are you easily discouraged by a tough situation? Do you find negatives or solutions? Can you venture a solution even if it might be wrong?

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