Odd Ball Interview Questions

Take a single piece of fruit out of the one marked "Apples and Oranges". Let us assume we've picked up an apple. Now, this box can't have both apples and oranges in it as that would make it correctly labelled, so this box must contain just apples.

This leaves us with the box marked "Apples" and the box marked "Oranges". One of these must only contain oranges, which obviously can't be the "Oranges" box, so the "Apples" box must be the one that contains only oranges. This leaves the "Oranges" box which must contain both apples and oranges.

Was just about to post this.

Anyway. These questions are about logic and lateral thinking. Sometimes it's more about making a decent fist of it than actually getting the right answer.

I did a special level physics paper back in the day. I remember a question about "Mary rides her bike to work, which is 5 miles from her house. How often will she have to change the tyres when the tread wears down?". The question was literally as short as that. So you get into making all kinds of assumptions and working from your basic world knowledge and how things fit together. I got a distinction in the end, so I must have been fairly good at guessing how quickly tyre rubber wears down...
 
As to the basketballs, calculate the volume of the room by measuring the length, width and breadth. A basketball is 29.5 inches in circumference, which gives it a volume of about 435 cubic inches.

Suppose the room is 12' x 12' x 8'. That gives it a volume of 1,990,656 cubic inches. Now, if spheres filled a room with perfect efficiency (i.e. no air gaps between them), there would be 1,990,656/435 = 4756.22 i.e. 4756 basketballs in the room.

Now, spheres don't pack together perfectly efficiently. The most efficient packing arragement is where you have staggered layers. This has a density of Pi/(2*sqrt(3)). Multiplying this by our original amount gives us 4150 basketballs in a room 12' x 12' x 8'.
 
Now, spheres don't pack together perfectly efficiently. The most efficient packing arragement is where you have staggered layers. This has a density of Pi/(2*sqrt(3)). Multiplying this by our original amount gives us 4150 basketballs in a room 12' x 12' x 8'.

If you can do this in your head then kudos to you!
 
One I know that we've given to graduates in their interview: "How many piano tuners are there in Chicago?"

Now obviously they're not expected to just blurt out a number and get it correct, the whole point of it is to see if the interviewee has decent logical thinking and problem solving skills - how they'd look at solving the problem is what counts not their actual number.


An ideal answer to it (which I've just stolen from the internet as I CBA to type it all out!) is:

  • There are approximately 5,000,000 people living in Chicago.
  • On average, there are two persons in each household in Chicago.
  • Roughly one household in twenty has a piano that is tuned regularly.
  • Pianos that are tuned regularly are tuned on average about once per year.
  • It takes a piano tuner about two hours to tune a piano, including travel time.
  • Each piano tuner works eight hours in a day, five days in a week, and 50 weeks in a year.
From these assumptions we can compute that the number of piano tunings in a single year in Chicago is
(5,000,000 persons in Chicago) / (2 persons/household) × (1 piano/20 households) × (1 piano tuning per piano per year) = 125,000 piano tunings per year in Chicago.​
We can similarly calculate that the average piano tuner performs
(50 weeks/year)×(5 days/week)×(8 hours/day)/(1 piano tuning per 2 hours per piano tuner) = 1000 piano tunings per year per piano tuner.​
Dividing gives
(125,000 piano tunings per year in Chicago) / (1000 piano tunings per year per piano tuner) = 125 piano tuners in Chicago.​



Another, far easier IMHO, question I've heard of graduates being given elsewhere is "Why is a manhole cover round?"
 
There's man carrying a brick standing in a rowing boat on a small pond, what happens to the water level of the pond if he drops the brick he is holding into the water?

(assuming there are no ripples caused by the brick or the boat bobbing, i.e. after the water surface has settled to being flat again)
 
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