>>1769
It took me a while but I think I get it now: you've generalised it as x^n. x^n is equal to the attached image. Alright! But yeah, still needs proof.

>>1771
Yeah that's what I meant. Sorry if it was unclear. I've tried the induction approach and I don't think it's the right way to go about it. I can't find any way to get it in the right form.

>>1771
I've got a hunch that you might be able to approach this via a combinatoric proof, specifically putting it in a form similar to that of "principle of inclusion exclusion".

Let x be the number of bins and n be the number of balls. Then the number of ways to put x balls into n bins is x^n.

We can try to count this in a different way: Form all bin-ball pairings (there are x*n) of these, and we pick n of these. This is (x*n C n). Now out of these there is a problem: not every ball among the pairings may a unique bin. Particularly,

1) Some pairings are invalid (ball 1 + bin 1 & ball 1 + bin 2) is invalid because ball can only go in 1 bin
2) Some balls may not appear in our chosen pairings

These are in a sense "complementary" issues. If we have a duplicate like (ball 1 + bin 1 & ball 1 + bin 2) there must necessarily be some other ball that is not chosen (because we choose n total pairings and we have n total balls).

Here's where things get sketchy and I'm not sure. It appears if we just solve the issue of "some balls not appearing in our chosen pairings" then we get the right answer directly.

We do that via principle of inclusion exclusion: we subtract out pairings in which at least one ball doesn't appear. If ball 1 doesn't appear then there are (n - k C n) possible pairings we could have chosen. Similarly if ball 2 doesn't appear, etc. so we have total of n * (n - k C n) things to subtract if one ball doesn't appear. But if just subtract this out we'll have undercounted the number of ways in which 2 balls don't appear, so we add back in (n C 2) * (n - 2k C n), and so on (this is standard application of principle of inclusion-exclusion. Reply back if this part isn't clear and I'll try to clarify).

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>>1773
Sorry for the triple post but I think I got it. The reason is that every invalid pairing corresponds to at least one ball being left out and vice-versa (the complementary thing I mentioned). So thus subtracting out all the invalid pairings is all you need to do.

Also to expand on the inclusion-exclusion stuff in case it wasn't clear, we want to subtract out "# of ways at least one ball is left out" which is "# of ways ball 1 is left out" union "# of ways ball 2 is left out" ... union "# of ways ball n is left out" which by inclusion exclusion is "# ways ball 1 left out" + "# of ways ball 2 left out" + ... "# of ways ball n left out" - (# ways ball 1 and ball 2 left out) - ... - (# of ways ball n -1 and n - 2 left out) + "# of ways ball 1 and 2 and 3 left out" + ... and so on (basically just think of a venn diagram).

Thank you for sharing the problem OP, it was interesting to think about.

I am pretty sure the fans on most graphics cards blow air into the heatsink, leaving it to exhaust out the side or back of the card, then sucked up by the rear fan. Not much you can do about that but I think it works fine most times unless the computer not designed for a large card like that. There are also blower style graphics cards which use a radial fan to blow air through a duct and out the back of the slot covers, which works better in tight computers, it's pretty common. I think a simple reason for making the card look nicer on the fan side would be that those images are what is mostly shown in product pages where people purchase the cards, so people will buy the better looking one regardless of if they'll see it in their case or not. Most computers don't have a clear panel anyway so the majority of the time the side isn't even seen.

Post edited on 29th Oct 2018, 6:12pm

>>1762
Air movement is more of a non-issue. The larger issues are generally going to be the heatsinks getting gunked up with dust. Make sure to blow out the dust every now and again.

With modern cases, there is plenty of room to prevent air from stagnating and heat up.

The real problem, as can be clearly shown in your image, is the PCIe ports being completely blocked. God forbid you want to use one of the new and fancy SSD drives, or a good quality sound card, or a network card.

Also, with multiple card set ups, you now have to remove everything to get to the card vice being able to lift out the problem card by itself. The cases and motherboards were designed with the vertical mount orientation in mind, both for air flow and ease of use. Changing that on a whim is a stupid idea, unless you *really* need to show off the LEDs on the fans of your graphics card which would be otherwise obstructed by another PCIe card.

>>1214
i disagree

>>1114
It looks like a joke even if you don't take it literally.

Just so people stop replying to this thread I'm gonna drop a knowledge bomb on you faggots.

It's called "Aerodynamics" and it's the reason airplanes have wings. You see, the wings generate lift by creating a difference in pressure, the shape of wings is such that air underneath is a higher pressure than the air over-top. Because pressure will always seek to reach an equilibrium, the higher pressure air will exert a force on the lower wing surface attempting to mingle with the much lower pressure air running over-top.

It is not the displacement of the engines that causes an airplane to travel upwards. This is idiot-proof when you realize that the engines are permanently mounted sideways, and couldn't possibly produce enough force downwards to generate lift.

The reason the airplane on a treadmill wouldn't work,(so long as the treadmill is rotating at a relative speed above the airplanes minimum take-off speed) is because it's airspeed is insufficient to cause a difference in pressure along the wing surfaces.

There is actually an effect similar to the treadmill mean in real aviation called "Tailwinds"; that is to say when the wind is blowing in a direction parallel to the planes travel, such that the wind is approaching from the rear to the front. It can, at sufficient windspeeds cause an otherwise airborne aircraft at the same engine displacement to stall and fall out of the sky, because the pressure differential under the wings is producing insufficient lift.

No, it will not fit between bars

It will inevitably lead to the extinction of humanity. I am all for technological advancement, but moving too far too fast is very concerning.

>>1704

Still a long, long ways away from singularity.

I'd welcome some innovative and new technologies, but everything for the last 3 decades has been iterative improvements to shit that already existed, combined with 'planned obsolescence' so that it stops working if you wait too long before buying the next iteration.

The end point of technology will be our destruction. Man is a cosmic accident, there is no point to us, but we still can function because our environment is still reasonably close to the original. Our biological programing still good enough for our situation. Yet more and more technology changes the game faster than nature can alter her program. Take obesity as an example, for nearly all of human history there was no such thing as a problem of constantly having too much food. In the last hundred years technology has made food abundant, making our own biological drives so suited to millions of years of hominid life moot. How will man's programed urges react to the new weights on the scales? What will happen when chance no longer is a major factor on human lives? What happens when most people become useless, when the systems we make outstrip their creators? What happens when we can alter genes freely. Or when we can alter people's moods, their minds, their capabilities? What happens when one can retreat into a virtual world to reign as God?

We will break ourselves. We will see what we really are. Living automata, a biological paradox, an abomination, an absurdity, an exaggeration of disastrous nature. Nature will no longer be able to correct her mistakes, we will be a species made almighty without, but equally a menace to its own well-being.

The results will be disastrous. Technology will peak when we can freely change one of two things, ourselves or the environment. In time those who change themselves will become infinitely malleable nothings, true Sartreans who's existence may blink out in an instant, both more and less than human. Those that seek not to change themselves but that which is external to them will retreat into virtual worlds, induced feelings, human similcra, a solipsistic suicide. In any case it will be nothing short of collective death. So long as technology advances faster than nature can create counter-measures, we will overshoot her target, blowing us apart in the process.

In genesis man's original sin was to eat from the tree of knowledge. Technology, fruit of knowledge, will perfect our fall. It will be a final complete fall where we shall lose even the memory of paradise. We will finally know ourselves for what we are, stand apart from ourselves look upon our species and find

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The ultimate goal of technology is replacing us, soft bags of suffering flesh into a trans-species capable of the great sacrifices needed for conquering the universe.

>>428
Well look how long internet explorer remained #1.
It looks like the most used browser by the lowest common denominator is owned by whoever dominates the tech industry at the moment.
This is most likely because they have enough of a monopoly to effectively promulgate it's supposed popularity amoungst the masses.

>>428
>>1668
To most people Google is the Internet. And when it tells them to switch to Chrome, they do as they're told. Not to mention the massive fear mongering campaign by the media that tells people they have to use the newest, most updated software or the evil Russian hackers will get them.

I've switched to Waterfox recently from Firefox ESR as it looks to be gaining ground after Moz-colon-slash-slash-a's insistence on screwing up. It's based off ESR56 and supposed to keep XUL intact alongside e10 so some old extensions will still work (can't live without Classic Theme Restorer and DownThemAll). Webextensions is restrictive garbage like the monoculture that spawned it.

>>1671
>can't live without Classic Theme Restorer
Just in case you don't know, you can modify a -lot- of the interface through CSS, way more than CTR ever could, with a couple exceptions. I was bothered by it too, but after testing Waterfox I just couldn't handle how outdated (and slow, YMMV) it felt so I sucked it up and only afterwards I found out about the editing. Just to be sure I reinstalled Waterfox and set it up like I had FF before Quantum, and my current edited Quantum felt and browsed way better. Sure, it's a lot more work as well, but it pays up.

If I ever use IE, this is going to be the reason 77.56% of the time.

>>1680
C

>>1680
A toss-up between C++ or VB, the latter because she's cutest and looks lonely, and the former because it's a langauge I actually use.

>>1680
Java is widely hated but still widely used. I have more experience with Java than any other language, though I'm trying to change that. It's verbose, has garbage collection, portable thanks to the JVM (with. couple exceptions), admittedly somewhat bloated, lots of documentation and libraries. Often seen as the poster child of the object-oriented paradigm, but has recently added more function features, such as lambda expressions. JavaFX isn't great, but it's easy enough to learn to make GUIs. One interesting thing about Java boilerplate and its verbosity is that you can write a hundred lines of Java that does essentially the same thing as a very short shell or python script. But it's still useful for a lot of things. I do think Java and OOP in general tend to overemphasize extensibility and modularity though. There are some bad design patterns and features in Java, like access modifiers or getters and setters. Not a big fan of that stuff. But it's a good way to learn about OOP and programming in general, like polymorphism, inheritance, control structures, and lots of other stuff I don't feel like writing out. Decent language despite all the flack it gets.

C++ is fast but easy to mess up with security and memory management. Widely used for things that depend on performance, such as games, but it just isn't worth the headaches. Learning C++ made me appreciate Java more -- garbage collection, references instead of pointers, and shit like that. For C++, you can use Qt or GTK. I personally never got into GUI development for C++, though I did for Java.

Python is okay. It's used for machine learning, Django (web dev backend), learning programming, and so on. "Forced indentation of code" is a meme on /prog/, since some people find it annoying that organization is syntax in this language. I'm surprised Python 2.X still exists, and it shows how making changes can cause fragmentation in a community. More people are adopting Python 3.X though, which is good. Paths for different versions of Python can be annoying. I've worked on a Project that involved a tool called Anaconda though, which made it easy for everyone to make sure th

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>>1638
>if you really wanted a language that will never go obsolete try Assembly
Terrible advice, considering the limited use-cases of Assembly, and also how CPU architectures change over time. x86 might be hot now, but it's being overtaken by ARM. Different CPU architectures have different assembly code. I learned MIPS assembly in college, and it's pretty much useless. I don't even put it on my resume.

>>1645
It appears as if this one was designed for GPU based crypto-currency mining for a large rig with many graphics cards.

>>1536
how does this image change when opened? what's that called?

There was a far higher proportion of fun and harmless viruses back in the day.

>>1688
I don't see how that's either fun or harmless.

>>1689
The author provided a crack that automatically cleared that score too, if I remember correctly.

Indeed, it has its days numbered. It's just a matter of time.

That's how it goes with everything. They have all the time and money in the world and they will salami and redo everything over and over until shit normalizes and goes through.
I don't know words strong enough to describe how disgusting and horrible this normalfag world is.
We're trapped in the belly of this horrible machine, but the machine isn't bleeding to death- we are.

The internet was a nice thing. Normalfags turned it into shit. Now other normalfags will it worse. Serves those cunts right. People complain about this killing small sites and businesses, but those same people likely only buy their shit from amazon anyway. They don't really give a shit about all the small sites and businesses that will be hurt, to them the internet is just a facebook youtube and reddit machine. If anyone really cared there would be riots on the streets. Instead you've got hipsters winning about paying an extra $5 a month for twitter on their $1000 iphones. Fuck those faggots. I long for the day when every nerd had their own webspace, when there were limitless things to explore and learn about on the endless sea of the net. We'll never have that again, but at least I can watch normalfags burn in the house they kicked us out of.

The way I see it, the big money maker, along with the biggest hog of bandwith are streaming sites like netflix, hulu, amazon video, etc. If internet plan segmentation happens, it's going to be for access to these types of sites. I would gladly pay for a lower tier of internet plan, that costs less, that doesn't allow access to these sites.

>>1495
Greenwashed bullshit. A 6kW set will set you back $15k and break even in 10+ years - that's excluding PV degradation, weather and battery replacements. I'd rather put that money into a low yielding fund and double it instead.

>>1669
Your tax money died for their sins.

>>1670
>break even in 10+ years
And by then the technology will be outdated with cheaper better stuff on the market. Not to mention the batteries would likely be toast by then.

I'm uneducated about energy extraction methods, which would be cheapest?
which would be eco-friendliest?
which would be most endurable?

>>1495
Now it's 2018, solar cell tech has been a bit more stagnant than we'd all like, and the US (one of the few major countries with enough empty desert to build massive solar plants in) still has tariffs on Chinese panels in some futile attempt to save some tiny domestic companies. I'm not holding my breath for a solar takeover in the next 20 years.

>>1683
Wind is very cheap, as in actually cheaper than coal and natural gas on real world grids where natural gas is subsidized instead of renewables, and it scales enough that it is the majority of generation in economies as large as the UK and Texas on many days. Capacity is still growing even after the US dropped rules that would have made coal fired plants more expensive.
I don't think anyone can confidently say what is most eco-friendly. Even if you replaced that extremely broad question with "what has the lowest effect on the greenhouse per Mwh generated" it's not straightforward. I don't want to shill wind too hard because it has obvious location limitations, but it's pretty great by this metric. Solar, hydro, and nuclear require a lot of energy to build (which for now means lots of fossil fuels burned), but have the potential to generate a ton of power in the equipment lifetime to offset.
Nuclear is theoretically the most enduring method if we're talking about the longevity of the equipment; that shit is supposed to be built to run indefinitely, but then people cut corners and it goes down in a natural disaster, and then other plants are shut in the ensuing political storm. Solar is of course on top if you mean the source itself, since if we switched to nuclear power we'd most likely run out of uranium before the sun dies.

>>1593
I ended up going to the .exe's properties for the game and checking disable desktop composition, haven't had the problem since.

Not exactly computer related but wasn't sure where else to ask. Any who, this might seem like a yahoo answers grade of stupid question but I need to know. Is there a difference between UV/black light and purple light? I have some RGB LED lights and don't want to damage my stuff with UV. If they're set to purple or blue, would it cause any negative effects?

>>1659
Yes, they both emit different frequencies of light within the electromagnetic spectrum, I recommend good ol' wikipedia, it's a fun read:
https://en.wikipedia.org/wiki/Blacklight

>>1659
UV light will probably have a negative effect on your figs. Similar to if you left it out in the sunlight.

Your UV lightbulb is probably low power, but extended exposure will have negative effects. A small amount won't be too bad though.

UV and red light have big difference in energy. UV carries energy enough to mess with the carbon-carbon bonds in your PVC or skin, which is why UV light causes sunburns.