# Mind boggling

Tags: , | Posted by Admin on 7/4/2012 9:16 AM | Comments (0)

The Googleinterview process is Infamous for it’s mind boggling and creative methods to test new candidates. Here are two I’ve selected for you to first try to solve yourself, then see Google’s perfect answer.

Q. How many golf balls will fit in a Mini?

A.

We will use a new mini opposed to a classic mini shape.

It is shorter than a person, so maybe its 4.5 feet high, but with the clearance off the floor, lets say roughly 4 foot. There’s space for two people to sit side by side, with roughly 2.5 feet per person. So that’s 5 feet wide. It’s probably two people long, which is approximately ten feet. However the bonnet takes up half the length, so the usable length is 5 feet. The interior volume, then, is about 4 X 5 X 5, which is 100 cubic feet.

A golf ball is somewhat bigger than an inch in diameter. Let’s say that 10 golf balls line up to make a foot. A cubic lattice of 10 X 10 X 10 golf balls, an even thousand, would just about occupy a cubic foot. That gives a quick answer of about 100 X 1,000 = 100,000

Or ….. take into consideration that each ball could be packed more densely given the shape of each. Effectively resting in an imaginary Lucite cude whose edges equal the ball’s diameter. You stack those Lucite cubes like building blocks. This would mean that the balls occupy about 52 per cent of the space. Break out of the imaginary Lucite boxes, and you can pack far more balls in a volume. This is an empirical fact. Physicists have done experiments by pouring steel balls into big flasks and calculating the density. The resulting random packing occupies anywhere from 55 to 64 per cent of the space. That’s denser than a cubic lattice. It’s also a fairly large range. How you fill the container matters. When the spheres are added gradually and gently, like sand pouring through an hourglass, the density is at the low-end of the range. When the container is shaken vigorously, the spheres settle into a denser packing of up to 64 per cent.

Where does this leave us? Someone willing to painstakingly stack golf balls in the cannonball pattern can pack about 42 per cent more gold balls in the mini than you’d estimate from a cubic lattice (or as above). That seems an absurd amount of labor, even for an absurd question. The reported density of stirred random packing is a more realistic goal. You might achieve that by pouring golf balls into the mini and stirring with a stick to settle them. That would give a density of about 20 per cent more than that of a cubic lattice. You might therefore increase your final estimate by 20 per cent, from 100,000 to 120,000.

For the record, the Mini website states a Mini Cooper Hardtop is 145.6 inches long, 75.3 inches wide (including mirror) and 55.4 inches high. The regulation diameter of a golf ball is 1.690 inches, give or take 0.005 inches.

Q. It’s raining and you have to get to your car at the far end of the car park. Are you better off running or not, if the goal is to minimize how wet you get?

What if you have an umbrella?

A.

To answer this question, you must reconcile two conflicting trains of thought. The case for running is this; the longer you are in the rain, the more drops fall on your head, and the wetter you get. Running shortens your exposure to the elements and thereby keep you drier.

There’s also a case for not running; In moving horizontally, you slam into raindrops that wouldn’t have touched you had you been standing still. A person who runs in the rain for a minute gets wetter than a person who just stands in the rain for a minute.

That valid point is mostly besides the point. You have to get to your car and there’s nothing to be done about that. Imagine yourself zipping across the car park at infinite speed. Your senses are infinitely accelerated, too, so you don’t slam into cars. From your point of view, external time has stopped. It’s like the bullet time effect in a movie. All the raindrops hand motionless in the air. Not one drop will fail on your head or back or sides during the trip. The front of your clothing will sop up every single raindrop hanging in the path from shelter to car.

When you travel at normal speed, you’re fated to run into those raindrops or, rather their successors. At normal speed, you also have drops falling on your head. The number of raindrops you encounter will depend on the length of your horizontal path and also on the time it takes to travel that path. The length of the path is a given. The only thing you can control is the time it takes. To stay as dry as possible, you should run as fast as possible. Running makes you less wet –provided you don’t have an umbrella.

Had you an umbrella as wide as a city block, and where you able to hold it, it wouldn’t matter whether you sauntered or sprinted. You’d be dry as toast.

Most umbrellas are barely big enough to keep the user dry when he or she is standing in general, vertical rain. In practice, you expect to get a little wet.

Umbrellas work by creating a rain shadow, a zone where there are no raindrops. In a vertical downpour, and with a circular umbrella, the rain shadow is a cylinder. When the rain is coming at an angle, the rain shadow becomes a skewed cylinder. However, as every seasoned umbrella user knows, its best to point the umbrella in the direction of the driving rain. This makes the rain shadow a proper cylinder again. Now pointed at an angle to the vertical,

The standing human body doesn’t fit so well into a slanted cylinder. Were a hurricane driving the rain at you horizontally, you would have to hold the umbrella horizontally, and a tree foot diameter would protect only about half your body. The rest would get soaked.

Wind is bad, and so is motion. The skilled umbrella wielder knows to tilt the umbrella forward, in the direction of the motion, to get the maximum coverage. In fact, wind and motion are indistinguishable as far as optimal umbrella pointing goes. Running at ten miles an hour in windless, vertical rain demands the same tilt as standing still in ten-mile an hour wind. Either way, the raindrops are coming at you ten miles an hour, horizontally, in addition to their downward velocity.

In vertical rain, you’re best off walking slowly. The umbrella will not have to be tilted much, and your body should fit within the rain shadow. Ideally, you should walk no faster than the speed where the rain shadow just covers your feet. Then you’d stay dry.

Reality is messier than that, there are always going to be gusts of wind, spatter from pavement, and runoff from the umbrella itself. The rain hitting the top of the umbrella does not disappear: it slides off the umbrella and falls in a cylindrical sheet encircling the rain shadow. There is more rain in that run off zone than anywhere else. That means that any part of your body that intersects the runoff zone gets wetter faster than it would have you not used an umbrella at all.

The umbrella has to be pitched at such angle that your lower body is out of the rain showdown. You’ll get half soaked no matter what you do.

All that reasoning boils down to the advice you may have heard from mum: walk if you’ve got an umbrella: run if you don’t.