Three job interview questions used by one of biggest companies in the world are incredibly difficult to solve
Here are three tough to crack interview questions that were once used by one of the biggest companies in the world.
Job interviews can be nerve-wracking enough when it comes to the basics - you know, 'what do you do in your spare time?', 'tell me a bit about yourself' and 'can you name one time where you had to solve a problem?'.
But add in some seriously tough brainteasers on top? Count me out.
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Well, that's exactly what would've happened if you'd have interviewed for PayPal back in the day.
We've all heard of PayPal before - the American financial technology company has been around for over 25 years and was a pioneer when it came to making online payments stress-free for users.
But did you know that the company was founded by three mega-successful entrepreneurs that are still around today?
Tesla and SpaceX owner Elon Musk founded the company with Peter Thiel and David Sacks back in 1998, going on to sell it for an eye-watering $1.5 billion (£1.2 billion) to eBay in 2002.
But back when the trio were running the company, it turns out that Musk, Thiel and Sacks liked to offer up some brain-teasers in interviews for potential employees.
These mathematical questions were claimed to be a staple of interviews at PayPal at the turn of the millennium, according to the book The Founders, by Jimmy Soni.
Here are the questions as laid out by The Guardian's Alex Bellos. Scroll down to the end for the answers.
Number divisors
Whole numbers normally have an odd number of unique divisors or an even number. Which whole numbers have an odd number of divisors?
A divisor of Z is a number that divides into Z.
For example, the divisors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. There are therefore eight unique divisors of 24.
Coin head scratcher
There's a circular table with an unspecified diameter and you and your opponent have unlimited identically-sized coins.
One at a time, you will take turns in placing a coin on the table - no coin can be moved after placing, and you can't place them on top of each other wholly or partially.
The first person that can't place a coin loses, what's your strategy to ensure that you win?
Burning ropes
There are two ropes, and each of their densities vary along its length, meaning they burn at different rates as the flame goes along, but they both take one hour to burn fully.
How would you use both ropes to measure 45 minutes?
Number divisors answer
The answer is: The square numbers: 1, 4, 9, 16, 25...
Read ahead if you're into maths and want the proof.
Let Z be a whole number, and D be a divisor of Z. If D is a divisor, then there is another divisor D* so that D x D* = Z.
So if you were saying Z = 24, then D = 2 and D* = 12.
You can pair off each divisor (D) with its complement (D*). The whole number should then have an even number of divisors unless the number is square, so in this case, there is a divisor D = D*.
But the question asked for unique divisors, so if D = D*, then it's only counted once. This also means that the total number of divisors for a square number will be an even number + 1.
Coin head scratcher answer
First, place your coin in the centre of the table.
Then, when your opponent places a coin, position it in the exact opposite place (180 degrees around the table centre) as there will always be space there.
Your opponent will eventually run out of space.
Burning ropes answer
Light both ends of one rope, and one end of the second at the same time.
The first rope will burn fully in half an hour, while there will be half an hour left to burn on the second rope.
Then, light the second rope from its other end - this will mean that the burning ends of the rope will meet after 15 minutes, making it 45 minutes since the start.
Joshua Nair