In the ultra-competitive world of graduate placement schemes, it isn't uncommon for employers to test candidates with near-impossible questions. One final hurdle allegedly presented to students hoping for a job with Microsoft in India, however, may have just topped the lot.

Prashant Bagdia, a Computer Science and Engineering student at the National Institute of Technology in Warangal, India, has shared a geometry question his friend was apparently asked at the final stages of an interview with the tech giant.

Here is the question in, well, question:

A right [angle] triangle has a hypotenuse equal to 10 and an altitude to the hypotenuse equal to 6. Find the area of the triangle.

Here's what that triangle might look like:

After a while suspecting the question may be a trick one, Bagdia's friend responded by using the formula most would apply: multiplying the base with the height, and dividing that answer by two. In this case, 10 x 6 ÷ 2 = 30.

As Bagdia reports on the question and answer forum Quora, the response didn't go down well:

"**Interviewer:** Are you sure? Think about it again!

**Friend:** Yes sir, I am sure the area of triangle is 30. You are just messing up with my brain to make me think otherwise so that I would commit error even in this trivial question."

The cocksure friend was wrong and failed to get selected.

"'The correct answer is, such a triangle cannot exist. If you think about it, you will come to know why!'" the interviewer is said to have told Bagdia's friend.

Bagdia goes on to explain that the question is a trick, because the hypothetical shape, with a hypotenuse equal to 10, could have an altitude of no more than five:

"The angle opposite the hypotenuse must be a right angle of 90 degrees. This means the two sides of the triangle must subtend a 180 degree angle in a circle. The hypotenuse must be the diameter of a circle, and the third point can be any point on the circle (except the endpoints of the hypotenuse)," he wrote.

"The vertical distance from the third point to the hypotenuse is the altitude to the hypotenuse. This is largest when the third point is at the top or bottom of the circle, and the vertical distance is equal to the radius of the circle (half the length of the hypotenuse, which is the diameter of the circle). Therefore, a right triangle with a hypotenuse of 10 can have an altitude on its hypotenuse of at most 5."

Another Quora user has since proven Bagdia wrong, albeit with a creative take on the problem.

Microsoft's trick effort is good, but is it the toughest question asked in an interview? Here are a few others that probably made people wish they'd never applied in the first place...

### 11 impossible job interview questions

**1. Estimate the total number of cars in the United Kingdom**

Reportedly asked at a Barclays interview. The answer, by the way, is around 30 million.

**2. “You have 17 red and 17 blue balls, and you remove 2 at a time. If the two are the same colour, add in one extra blue ball. If they are different colours, add in an extra red ball. What colour is the final ball removed?”**

A test set by lottery games manufacturer Geonomics. Not worked it out? It's always red. We think.

**3. “What's your favorite 90s jam?”**

Asked by US tech firm Squarespace. There are just so many to choose from.

**4. Describe the colour yellow to somebody who's blind.**

Spirit Airlines get philosophical.

**5. “If you were the Head of Barclays Corporate what would your strategy be with the recent European Crisis?”**

Barclays again, looking for advice.

**6. When a hotdog expands, which direction does it split and why?**

Asked of a candidate applying to be a SpaceX Propulsion Structural Analyst – which is a title that could probably put most off. The answer, by the way, is that sausages always split lengthways, for reasons that are far beyond our comprehension.

**7. What would be the name of your debut album?**

Asked by Urban Outfitters, obviously.

**8. There are 25 horses. You can take 5 of the horses at a time and race them. Each horse always finishes the race in the same amount of time, and there are no ties. The only information you get from each race is the order that the 5 horses finished in. What is the smallest number of races you need to find the 3 fastest, in order?**

Asked of Quora user Michael Tan in an interview once. The answer, we are *almost entirely sure*, is seven.

**19. Imagine we are playing Russian roulette using a standard 6-chamber revolver. I put two bullets in the gun, in adjacent chambers (i.e. chambers next to each other). I spin the barrel and take a shot. Click. I pass the gun over to you. Do you take the shot, or spin the barrel?**

A favourite on Wall Street. The answer? Probability dictates you *should* spin again.

**10.** **F O R T Y + T E N + T E N = S I X T Y **

**Each letter represents one of the digits from 0 to 9. Determine which digit corresponds to which letter.**

It's 29786+850+850=31486. Memorise that, and the method.

**11. If you had $2000, how would you double it in 24 hours?**

Uniqlo favour this test. Presumably the right answer is 'sell loads of clothes'.