Here’s one that you might run into when being screened for a technical position: the brain teaser. The point here, usually, is not to see if you can solve a riddle. But more to see how your mind works when an unusual problem arises (see it as creative problem solving). I’ll go over some of the types of questions you may encounter and I’ll also give some references for who like this kind of stuff .
The answers to these kind of questions are based on estimates and a logical thought-process that accompanies these estimates to derive a valid answer. Often you won’t find the correct answer, but the idea is to get very close. Some of the popular Fermi-questions are: “How many piano tuners are there in the world?” or “How many gas stations are there in the United States of America?”. A bad way to answer these questions is to just give a number and be done with it.
On wikipedia you can find a good example of this: “How many piano tuners are there in Chicago?”
Next to wikipedia, here is another great resource on the subject: Science Olympics. Here you will also find many examples of Fermi-problems. Some neat ones:
- How many golf balls will fit in a suitcase?
- How many hairs are there on a human head?
- If your life earnings were doled out to you by the hour, how much is your time worth per hour?
- People crowd into London until all available open space within the city limits is covered with standing people. How many people would there be?
More information about Fermi problems in general can be found on Wikipedia.
These are actually just weird questions. Again, keep in mind that the purpose of these questions is to see how you approach a problem that is new to you. For instance: “How are m&m’s made?”, “Without looking at specifications, what is the weight of a Boing 747?” “Why are soda cans produced in that shape?” “Why are manhole covers round?”
Some of these questions can be about things that you know. If you know how m&m’s are made, just answer. If you just now looked at you soda can and asked yourself “Why is it made like that?”, you might want to do some thinking. The answer can be simple: They are made like that cause that way they stack easy. The answer can also be scientific: The curves in the can make sure that the build up pressure inside the can doesn’t make the can go boom. If it would be a metal cylinder with the same thickness of steel everywhere, the can probably can’t stand the build up of pressure inside the can.
These questions often have a certain way of looking at a problem to find the solution. Typically, with these questions, when someone gives you the answer you go “aaaahhhhh…of course”. A very famous one here is the riddle that John McClane (played by Bruce Willis) and Zeus Carver (Samuel L Jackson) had to solve in Die Hard: With a Vengeance: You have a jug that can contain 5 liters (let’s call it J5) and a jug that can contain 3 liters (J3). Now, you need to get exactly 4 liters in the 5-liter-jug. Solution (let’s use water, just like in the movie ):
- fill J3 with water
- poor J3 into J5
- fill J3 again with water
- fill J5 to the top (now you added 2 liters, so you have 1 liter in J3)
- empty J5
- fill J5 with the 1 liter from J3
- fill J3
- poor J3 into J5
And now J5 contains 4 liters of water.
Another one: You have 8 billiard balls. They all have exactly the same weight, except for one. You have a weighing scale like this:
You need to find the billiard ball that has a different weight with the least amount of weighings.
Answer: You can find the billiard ball in two weighings.
Put three billiard balls on each side of the scale. If the scale balances to a side, you know in which batch of three the crooked ball is. Now you put one ball of this batch on each side of the scale. If it balances to a side you know which ball is crooked, if it doesn’t, the crooked ball is the remaining one. If in the measurement of 3 versus 3 the scale stays in balance, you just need to measure the remaining two.
This can also be done with 9 billiard balls, here when the scale balances to one side in the first weighing, the crooked ball is in the last batch of three. And you still have to just weigh two of them to find the crooked billiard ball.
As you can see, there are many examples of these kinds of questions. You can spend a lot of time surfing the web searching for these questions.
There are also several books that cover this subject. Often these books also cover other subjects I talked about in these series (algorithms, programming questions,…)
- How would you move Mount Fuji?(William Poundstone)
- Programming Interviews Exposed (John Mongan, Noah Suojanen, Eric Giguère)
- Puzzles for programmers and pros (Dennis Shasha)
- Cracking the coding interview (Gayle Laakmann)
…and probably many more