There is a famous thought experiment/cliché that says that if you have a million monkeys, typing on a million typewriters, for a million years, then through the power of sheer randomness, they will at some point type out the complete works of Shakespeare.
The reason that this is supposed to work is either to demonstrate that in a very very large data set, pockets of order spontaneously arises from out of the chaos. The other reason that this is supposed to work is because of the Law of Large Numbers, which says that if you perform an experiment often enough, you will get the answer that you are looking for. Basically this a corollary of the premise that if the probability of an event not happening is P-x, then P-x ^ infinity tends towards zero. If the probability of an event not happening on an infinite time scale tends towards zero, then the probability that same event happening at all, must also tend towards one.
Apart from the problem that 1,000,000,000,000,000,000 (pentillion) monkey hours is hard to arrange, that all of the monkeys will have eventually died, that all of the typewriters will have eventually ceased to work and rusted away, we have already invented a device to do this and performed the experiment. It is called "The Internet".
Let me run you through this prime piece of monkey thinking in the howl-house we call the internet (from Twitter):
What's the strangest question you've been asked in a job interview?
- Tess, 21st Monkeber 20XX
In response to this came:
How many windows are there in London?
Why are manhole covers round?
- Mokujin, 21st Monkeber 20XX
Oh dear. What a thing to have uncovered. This very much reminds me of the name of one of Andy Zaltzman's comedy shows which was called: "Andy Zaltzman Opens The Door, Is Horrified By What Lurks Behind, And Closes The Door Again." I fear that I have stumbled across a manhole shaped door, opened it, and have been horrified by what is lurking behind it, waiting to come out.
And thus, our million monkey typewriter device was primed with its input and set off on its dastardly jaunt all over the world; ignoring Logic Town and instead stopping at West Banana, Nonsense Central, taking the Diversion Loop to Barking Mad, before rejoining the main line and stopping at Opinion, Theory, Assertion, Lies, and all stations to Great Irrelevance. I love these rides on the million monkey typewriter device.
Why are manhole covers round?
It’s the only shape that can fall into itself, so the cover can’t fall into the hole even if angled differently.
The logic behind this 49 reply monster is that if a manhole has radius r, then a round manhole will have the longest chord of 2r. The manhole cover itself, which needs to be 2r+n (where n is some amount which is marginally bigger than the width of the hole) can never fall into the hole because 2r+n - 2r = n.
Our old friend Pythagoras will tell you that the longest chord length of a square manhole, will be 2√2r. There are orientations of where a square manhole cover can fall into a square manhole since 2√2r+n - 2r+n = some value at about 80% of r which is absurd.
This is where the million monkey typewriter device truly shines. Example, counter example, theory, counter theory, anguish, outrage, snark, and all stations to Great Irrelevance.
The thing that I love about this is that the whole discussion in 49 replies, seems to have conveniently forgotten that out here in the real world, the vast majority of manholes are in fact either square or oblong.
The general truth about covers/doors/caps out here in the real world, is that covers/doors/caps are are generally are the same shape as the hole that they are covering. Admittedly there are edge cases here where the doors exist, purely for legal reasons such as old-timey saloon doors.
At this point, also cue stories about hotels in the Wild West, about doors in front of kitchens, about car doors, jokes about Irish people in the desert, stories of the London Undergrounds doors that curve into the ceiling, passimiter gates, and a tale about someone's cat called "Manhole" who is cat shaped.
We even had a lovely philosophical discussion about the telos of the question itself where someone quite rightly (I think) suggested that the questions were asked because the HR Department doesn't really care about the answer and just wanted to see prospective candidates' ability to think and work out problems logically under pressure. That could very well be true however another answer posited was that really all this was was a chance for the person in the HR Department to engage in top bants and decide whether or not they liked the prospective candidate. I think that the truth lies somewhere in here.
This leads me to answering the other question which was mostly ignored and forgotten by out million monkey typewriter device.
How many windows are there in London?
Well...
I read the news today; oh-boy.
4000 holes in Blackburn, Lancashire.
And though the holes were rather small,
They had to count them all.
Now they know how many holes it takes to fill the Albert Hall.
I have no idea how many holes it takes to fill the Albert Hall but "they" do.
What I do know is that London is bigger than Blackburn; ergo, it must follow that there are more holes in London than Blackburn. Since some of those holes are going to be windows, filled in by panes of glass, then I think that it is fair to say that there are more than 4000 windows in London.
And yet again, I have contributed to the output of the million monkey typewriter device. To be perfectly pedantic (and yes, my whole professional life has been working out of offices on Pedant Corner), we already have typed out the complete works of Shakespeare. The chances of a thing having happened, which has already happened, is one; by virtue of it already having happened.
Go monkeys!
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