No, really: stop me if you’ve heard this one before

Silicon Alley Insider is running an article titled 15 Google Interview Questions That Will Make You Feel Stupid. Several of the questions are interesting, but several are chestnuts that if you know puzzles, you barely remember where you heard them the first time. On the other hand, if you aren’t a puzzle person you’re not likely to solve them quickly and under pressure during a job interview, making them less than useless. It doesn’t help that the article doesn’t display a good understanding of the puzzles, and gets several answers wrong.

Here they are:

Stupid Interview Questions

Wanted: Boys

In a country where people want only boys every family continues to have children until they have a boy. If they have a girl, they have another child. If they have a boy, they stop. What is the proportion of boys to girls in the country?

This one is perhaps interesting from a can-you-be-misled standpoint: since the probability of any given child being a boy or girl hasn’t changed, the overall proportion can’t be changed by decisions you make after the child is born. It’s a nice puzzle, but I first heard it at least ten years ago. If you know puzzles, you (almost certainly) know this one.

Manhole Covers

Why are manhole covers round?

Seriously? This is supposed to make you feel stupid? Again, if you have any interest in puzzles whatsoever, you’ve heard this one before. The answer to give is definitely not the one they give — so they can’t fall in — at this point that’s trite. The trick now is to come up with some other answer that has at least some plausibility: making them round makes it easier to move them by rolling them since they’re heavy; a round hole makes sense from a “get the most access for the least hole” standpoint; round holes are sturdier and easier to dig; a circular cover doesn’t need to be oriented before being put in place. Or point out that any shape with a constant diameter will prevent falling in, the most common being the reuleaux triangle. Or if you want to be cheeky point out that not all countries use round manhole covers.

Handy

How many times a day does a clock’s hands overlap?

I actually like this one, old as it is. For some reason the answer never sticks in my mind (now that I’ve said that it will) and I have to think it through. Sometimes I even get it wrong :-)

Thinking Laterally

A man pushed his car to a hotel and lost his fortune. What happened?

A classic lateral thinking (or situation) puzzle. Generally these are followed by a series of yes/no questions to attempt to figure out the intended meaning of the misleading original clue. Obviously the interviewer’s goal with this is more to see how clever you are at asking questions rather than how quickly you can solve the puzzle; but again, if you know lateral thinking puzzles this one isn’t going to pose much of a challenge (I solved it after about fifteen seconds, obviously without asking any questions, and I’m not even very good at lateral thinking puzzles), and if you don’t know about them, you’re unlikely to make much of an impression with your question-asking.

Logical Pirates

You’re the captain of a pirate ship and your crew gets to vote on how the gold is divided up. If fewer than half of the pirates agree with you, you die. How do you recommend apportioning the gold in such a way that you get a good share of the booty, but still survive?

The answer they give here is just plain wrong. The wording of the puzzle itself is weak as well. This puzzle is at least five years old (albeit a good puzzle) and fairly well-known. It’s ridiculously hard to solve on the fly and fairly likely to be known by anyone interested in puzzles. The puzzle is usually put something like this:

There are five pirates on a ship, with 100 gold pieces to divide between themselves. The pirates are logical, self-preserving, greedy, and bloodthirsty in that priority. They agree that they will each in turn propose a way to divide up the gold, starting with the captain. If the majority of the pirates agree with the proposal, that is how the gold will be divided. Otherwise the pirate making the proposal will be tossed over, and the next in terms of seniority will make a new proposal. What proposal should the captain make?

To find the answer, number the pirates and work backwards:

4. If it comes down to pirates 4 and 5, then 4 is out of luck; even if he proposes giving all the gold to 5, 5’s bloodthirsty and he’ll say no, kill 4, and take all the gold.

3. If it comes down to 3, 4, and 5, 4 will vote yes to 3’s proposal no matter what, in order to save his own life (see 4 above). Therefore 3 can propose that he (3) gets 100 pieces of gold and 4 will vote yes, and the proposal passes.

2. If it comes down to 2, 3, 4, and 5, since 4 and 5 get nothing under 3’s proposal, 2 can propose 98 pieces of gold for himself and 1 each for 4 and 5, and they will vote yes, giving a three-to-one majority.

1. Therefore the captain, pirate 1, should propose 97 pieces of gold for himself, 1 piece for 3, and 2 pieces for either 4 or 5, and have a three-to-two majority.

Ballsy

You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you find the ball that is heavier by using a balance and only two weighings?

Seriously, I first encountered this puzzle in a book my parents gave me when I was eight. Guess I should have applied to Google back then, eh?

Egg Drop Soup

You are given 2 eggs, which are identical. You have access to a 100-story building. Eggs can be very hard or very fragile, which means the eggs might break if dropped from the first floor or might not even break if dropped from 100th floor. You need to figure out the highest floor of the 100-story building an egg can be dropped from without breaking. The question is how many drops you need to make. You are allowed to break the 2 eggs in the process. (I’ve now updated their wording to correct their grammar and make it clearer)

As with the pirate puzzle, the answer given is incorrect (Update: their answer has been corrected). The correct answer is 14 drops.

You start on the 14th floor; if the first egg breaks there you start at the first floor with the second egg and work your way up each floor, potentially to the 13th floor.

If the first egg survives the 14th floor, you go to the 27th: thirteen (not fourteen) floors higher because you burned a drop on the 14th floor. If the first egg breaks there you start at 15 and try each floor from there potentially up to 26.

This pattern continues. If the first egg survives, you go up twelve floors to the 39th, eleven to the 50th, and on to the 60th, 69th, 77th, 84th, 90th, 95th, 99th, and finally the 100th.

Note that 13 drops is not possible; if you start on the 13th floor (and the first egg survives) you will reach the 88th floor, then the 90th, then the 91st, and be out of luck.

Shrinky-dink

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?

The answer given here is wrong. “This one is all about the judging interviewee’s creativity.” No. This is all about understanding physics. Again, this is a common puzzle. As any seasoned puzzler will tell you, if you maintain density and proportions, your strength decreases as the square of the change, but your mass decreases as the cube of the change. So you would simply jump out of the blender. Trying to break the electric motor as suggested would be far less possible than it would be if you were full-sized, i.e. impossible (since you wouldn’t be able to throw it).

Conclusion

Interview puzzles fail on two fronts: for anyone who has a taste for puzzles, you’re more likely to give them a puzzle they already know than to truly stump them; and for those who don’t happen to like puzzles, your attempt to find out how clever they are is more likely to simply frustrate them and mislead you. Finally, asking more difficult/obscure puzzles perhaps solves the first issue, at the cost of making the second issue far worse.

That said, I love interview puzzles in general, so bring ‘em on!

7 thoughts on “No, really: stop me if you’ve heard this one before

  1. Jim Martin

    I know I’m commenting on the wrong article, but I was wondering if you could give an update on your diet, exercise regimen, and recent lab work? I really enjoyed your articles about how your low carb diet drastically changed your labs and weight.

    Also, could you please tell me if there is room for alcohol in your diet?

    Thank you very much.

    Jim Martin

    Reply
  2. gcanyon Post author

    You saw the update a few months ago? http://gcanyon.wordpress.com/2009/08/05/cholesterol-update-low-carb-plus-exercise-good-health/

    I’m still doing it, although I just moved to St. Louis and it takes time to figure out where to get reasonable fast food, etc. especially since I’m on foot here.

    Also, in general I’m not taking it as seriously as I did. Since my weight/bodyfat reached a reasonable minimum, I’m curious to see if backing off a bit on the diet has a detrimental effect on my cholesterol. I’ll probably get another blood test in December and post then.

    I can’t help on the alcohol front — I’ve never had any. Guess I should do an entry on that.

    Reply
  3. jon

    For the Egg Drop, I’m completely lost as to how you got your answer. Please explain. I don’t see how you knew to start at the 14th floor. Also, you say:

    “If the first egg survives the 14th floor, you go to the 27th: thirteen (not fourteen) floors higher because you burned a drop on the 14th floor. If the first egg breaks there you start at 15 and try each floor from there potentially up to 26.” Then you go on to say:

    “If the first egg survives the 14th floor, you go to the 27th: thirteen (not fourteen) floors higher because you burned a drop on the 14th floor.”

    I don’t see how you burned a drop on the 14th floor since you just stated the first egg survives the 14th floor drop. Furthermore, I don’t see where you came up with the pattern.

    Reply
    1. gcanyon Post author

      @Jon: remember, the goal is to minimize the number of drops, not the number of eggs used. You only have two eggs, and you need to be certain that you find the exact floor where the eggs will break. So if at any time you break an egg, you have only one egg left. At that point you must start just one floor above whatever the highest floor you know an egg can survive, and go up one floor at a time.

      So if the first egg breaks on the first drop from the 14th floor, then you must start with the remaining egg on the 1st floor and go up one floor at a time. If you tried skipping a floor, say, going from the 5th to the 7th, then if the egg broke on the 7th floor you wouldn’t know whether an egg could survive a drop from the 6th floor, and you’re out of eggs. So going up one floor at a time, you’d use as many as 14 drops: the first drop from the 14th floor, and however many floors it took to break the second egg (or perhaps the second egg survives the 13th floor, meaning that the 14th is the floor the eggs break on).

      Now suppose the first egg survives the 14th floor; how many floors up could you go then? It’s not 14. If you jumped from the 14th floor to the 28th floor and the first egg broke, you’d need to start from the 15th and go up floor by floor, and possibly the second egg would survive all the drops up to the 27th floor. That would be a total of 15 drops: the first egg from the 14th and 28th floors, and the second egg from the 15th through the 27th floors (13 drops). To ensure that you would use only fourteen drops, you can only go to the 27th floor with your second drop of the first egg.

      Likewise, if the first egg survives the first two drops, at that point you have used up two drops, so you can’t drop the first egg from 14 or even 13 floors further up; you can only go up twelve floors.

      I hope you can see the pattern at this point: for each time you drop the first egg, you can go up one floor less because you need to keep the total drops down to fourteen.

      As for how I knew to start at 14, I could throw out some equations, but the reality is that I guessed (16, I think), and optimized from there.

      Reply
  4. Tom Dignazio

    The answer to the egg problem is 1. It’s a common sense question, not a math problem. Anyone with common sense knows an egg can’t drop 10 feet without breaking on the sidewalk.

    Reply
  5. Pingback: 20 Interview Questions You’ll Be Asked At Google

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s