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Number theory's not really my thing, but I think I have a good candidate for the "maximally interesting" function for k. Choose k = n/ln(n). The inspiration comes from the prime-counting function. The number of primes less than n is approximated by n/ln(n) and since we basically want the numbers in our set to be coprime so that their product is maximized, the problem is effectively reduced to "find all prime numbers less than n". In fact, it's even a little bit harder than that because there may be more or fewer primes than that. If we use the sieve of Eratosthenes, these primes can be found in O(n*log(log(n))), which is actually pretty efficient. (I don't know if the SoE is the most efficient algorithm-- I've heard that there are optimizations of it but I don't know if they affect the overall time complexity.)
OmnipotentEntity, would you be so kind as to produce a graph of ak(n)*(k/n)^k vs. n where k is round(n/ln(n)) and "round" refers to rounding to the nearest integer?
Edit: With regards to OmnipotentEntity's question below...
OmnipotentEntity wrote:
Well, because of combinatoric explosion, the larger values of i and n tend to make computation longer. However, this cannot be what you mean. Can you elaborate?
I disagree that larger values of i tend to make the computation longer. If we have i=n, there is exactly one partition in which we use n 1s. If we have i = n-1, it's the same story-- n-2 1s and one 2. Things get ever so slightly nontrivial when we have i = n-3, in which case we could have n-3 1s and one 3 or n-4 1s and two 2s. Clearly, an-3(n) should always be 3 for sufficiently large n because the second 2 would not contribute to a larger LCM and we therefore want that 3 in there.
Anyway, I just mean to illustrate that the partitions are maximally complex for intermediate values of k (or i).
Edit 2: My candidate function of n/ln(n) is fine, but I now see that a much better approximation of the prime-counting function is li(n), the log-integral function, which is the integral from 0 to n of dx/ln(x). I mistook the two functions as identical. OmnipotentEntity, if it's not too much trouble, could you (instead) produce the graph I requested except using round(li(n))? I'd do it myself, but I don't really have a good program to do it in at this time.
Edit 3: Incorrectly defined the li function. Also, FYI, I'm working on producing a graph ak*(k/n)^k vs. n when k = li(n). I'm using Scilab, which I forgot I downloaded but never used much. I'm not sure I'll be able to figure it out on my own, however.
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I think that FractalFusion and OmnipotentEntity may have misinterpreted my post. My goal is not to find a function for k in terms of n that maximizes ak(n) (which would be k = n/e) but rather to cause the wildest fluctuations in ak as a fraction of (n/k)^k. As I suggested, we can begin our investigation with two sample functions:
k constant. In this case, we expect ak(n)*(k/n)^k to approach 1 because we should be able to find the k values that maximize their LCM really close to (n/k) for large n. For example, if I'm partitioning 1,000,000,000 into 10 pieces, I should be able to find all 10 numbers really close to 100,000,000. Searching for these 10 values would also take a relatively short amount of time since we know to look near 100,000,000. Because the asymptotic behavior is well-behaved and the maximum LCM can be efficiently computed, I characterize this function as, in some sense, trivial.
k ~= n. In this case, we expect ak(n)*(k/n)^k to approach 0 because our partition will naturally contain a lot of 1s. I may be wrong, but I think that for sufficiently large n, the growth of (k/n)^k being exponential will vastly outstrip the relatively slow addition of 2s, 3s, and larger numbers to our partition. Again, we have a pretty good idea of how to find our partition that maximizes the function: start with k 1s, then add the remaining n-k units throughout the partition, preferentially bringing elements of the set up to prime numbers. As with the above function, this is both easy to approximate and easy to compute a partition, so I again characterize this function as trivial.
But something interesting must (?) happen somewhere in the middle. There should be a function of k in terms of n that, when we try to find the partition that maximizes the LCM, is a complete nightmare. It may even require including many elements in our best partition that are not coprime, resulting in wild fluctations in ak(n)*(k/n)^k.
I must make two concessions. First, I have to admit that I didn't understand many of OmnipotentEntity's graphs. Could you be more explicit about what you're graphing at each step? And second, I've used some really squirrely language throughout this post. I can't really attempt to define "wild fluctuations" or "interesting". The closest I can come is where I say finding the right partition is "a complete nightmare". In this sense, I suppose I would be looking for the function k in terms of n that maximizes the computational complexity of finding the partition that maximizes the LCM. But perhaps that's distinct from the the function that produces the wildest fluctuations in ak(n)*(k/n)^k. I hope that's more clear.
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OmnipotentEntity wrote:
According to OEIS, the asymptotic behavior of ak(n) seems to be nk/kk. I do not know why this would be the case.
I actually think this is fairly intuitive. For large n, the partition Pk(n) that results in the largest LCM would be one "near" a distribution where all k elements are close to n/k. For example, if I want four numbers that add to 100 and multiply to the largest possible value, I would make them all 25. The LCM function just mucks them up a little bit and so I might choose something like 19, 25, 27, and 29, numbers all clustered around 25. (The LCM of these numbers as a fraction of (100/4)^4 is 0.95.) One expects that for sufficiently large n relative to k, these numbers will be arbitrarily close to n/k. There are k such numbers in the set, so multiplied together, we get (n/k)^k. This gives us an idea of how to search for ak(n); start with all elements around n/k, then redistribute the values slightly until we reach k numbers that are coprime.
What I think is interesting is that for k<<n, ak(n) settles pretty closely to (n/k)^k for the reason I outlined above. For k~=n, we can also see that ak(n) is pretty well behaved because your partition is going to become saturated with 1s. There should be a "sweet spot" for k (as a function of n) that makes this function in some sense "maximally interesting", where the partition that produces the greatest LCM is extremely nontrivial and does not settle down for large n. I'm going to guess it's something like k = n/2 or k = sqrt(n), but since I haven't really defined this sweet spot, I'm not quite sure what to look for.
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I'm sure that this has been asked in one of the other submission threads, but why bother hitting the springboard in 8-2? I noticed that you end the level with the last digit of the timer at 2, so I understand that skipping the springboard would need to save over a second for it to make a difference. Is that what's going on?
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I've never coded an emulator myself, but I'd start with assembly language, since your main goal is emulating the system's processor. The other thing you should probably understand is hardware architecture so you know how all the pieces fit together.
Far more learned people will be along to answer your question shortly.
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Nach wrote:
I'm wondering if this is due to some having poor silicon in their CPUs which under-perform, power saving settings, or if various browser plugins or perhaps active browser tabs are slowing down operations being benchmarked.
That's my theory. I have over 100 tabs open.
It's a bad habit...
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feos wrote:
Wow, you can't stop aiming at my personality instead of my arguments. Doesn't look like what a "halfway decent mathematician" would do given the potential policy issues. Moth resolved most of my complaints. You resolved none.
Did you know that forum discussions are for people who care and at the same time have something to say? I've probably been a part of all policy discussions during the last few years. Some people even liked that. Some of my policytweaksuggestions have been implemented as final decisions. Not because I'm powerful. But because I cared, had something to say, and what I said appeared to be practical. So I dunno why things I say are automatically discredited by the fact that I'm the only person in the thread saying them.
you are literally the only person who has stamped his foot to say, "This is a bad idea?"
I never said the idea is bad. It'd be nice to have a list providing movies not present in any other lists, and/or a list of non-vaultable runs. But it has issues to resolve. If your solution to them is "only feos complained about them so it's all fine", I pity you.
Come on, man. Don't be a jerk.
As you said, Mothrayas has resolved most of your complaints, so what's my role here? You want me to address your arguments? Okay, let's return to this point:
feos wrote:
"Not [random pile of tags]" is not a sensible definition of a movie tag.
The tags I listed were not "random". I think they form a pretty comprehensive list of common tags that we affix to movies regarding their stated goals. Did I miss one? Fine, tack it on to the list. (I just checked. I guess I missed "Aims for maximum score". There are a few others, but I consider "Demonstration" synonymous with "Playaround" and tags like "Aims for in-game time instead of real-time" to be an augmentation of a primary goal.) So if my definition is "anything that doesn't fall under the other primary goal tags", it's not random and it's not arbitrary.
And I'll remind you, if someone wants to interpret the tag differently, hey, that's fine too. It's still a good tag even if it's not implemented in exactly the manner I would use.
Finally, I've worded this statement really carefully throughout the thread: I would like to see someone weigh in against this idea in addition to feos. I'm not disregarding your idea because you're saying it; if that's what I had meant, I'd have instead typed, "... instead of feos." But ultimately, your reasoning comes across as circular:
"People will complain about this!"
"Who?"
"I'm complaining about this!"
As of right now, you're the only barrier to this being implemented, and before you jump in to say "Nach and adelikat are barriers too", no they're not, they just haven't been consulted yet.
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Demon Lord wrote:
I understand that it comes down to "Not (tag1 or tag2 or ... tagn)", so, in other words, "special goal" means "other"?
Yep.
feos wrote:
By undefinable I mean than it can't be put in a way equally meaningful for the vast majority of our users. You've probably never seen users raising flamewars over a definition. Since this place is in a way geek-oriented, you have to have solid rules for things.
If that's so true, shouldn't it concern you that you are literally the only person who has stamped his foot to say, "This is a bad idea?" I entered this thread saying I wanted to hear arguments against this idea from someone in addition to feos. I'm still waiting. You're operating under the assumption that all this bickering and flaming is going to come out of the woodwork after we implement a special goals tag. I appreciate a dose of skepticism and concern, but at some point, someone else needs to step forward in agreement with you.
What's the harm in it, really?
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feos wrote:
"Special goal" as a term means nothing other than not something. If you want it to include everything that wastes time compared to vaultable goal, it's at least definable. If you just want it to contain everything that's not yet present in the existing tags (or some other variant), it's undefinable, and arbitrary in where you draw the line.
The latter would be more useful if it could be defined, because it would contain stuff other tags miss, but I dunno how realistic it would be.
Any halfway decent mathematician will tell you that a definition through negation is still a perfectly valid definition. The same should be true for this website; it's not enough to say, "This category is undefinable because the definition you've given me makes me uncomfortable."
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Niamek wrote:
I don't think it should be included.
But for the sake of a clear definition, they'd probably need to be included.
I dunno about that.
Any% - Completes the game as fast as possible.
100% - Obtains all collectibles (or similar) as fast as possible.
Low% - Obtains the fewest collectibles, second priority is beating the game as fast as possible.
Playaround - No specific goal. Glitch exhibition.
ACE - Injects arbitrary code as fast as possible. Movie is longer to showcase the code and that it is, in fact, arbitrary.
Special goals - Anything not falling into the above list. Usually game-specific goals that that are not associated with tracked collectibles and achievements.
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grassini wrote:
"catch em all" or "diploma" feels like 100%,just saying
Also,"special goals" feels like "playarounds" lol
I've been thinking since near the start of this discussion that one of the key points that I don't believe has been properly emphasized is that movie tags aren't all that important to the website. That's not to say they're unimportant but rather if a movie is miscategorized, is it really going to drive anyone away from the site? Personally, I would rather see a tag implemented inconsistently (within reason) than not implemented at all. For example, I may not be able to pull up every movie that features heavy glitch abuse, but I like that I can see what is at least a representative sample.
Anyway, if I may steer the discussion on a tangent, this has gotten me thinking about how important various aspects are to the website. I don't think we would agree on everything's importance in absolute terms, but perhaps we can do the next best thing and mostly agree on relative terms. Here's my rough list of most to least important subjective aspects of movie publication, off the top of my head:
Judging
Emulation
Submission text
Encoding
Publication text
Discussion of the movie
Tags
User ratings
User votes
Game resource pages
Other forum discussions
(Did I miss anything?)
Entries near the top of the list are things that it is important the site both "does correctly" and "does not do incorrectly" (whatever that may mean in context), while entries near the bottom are less crucial to the reputation, popularity, and overall healthiness of the site.
I'm curious how other members might shuffle items around. How would you prioritize things?
(It may be appropriate to split this off into a separate thread if discussion picks up along these lines.)
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I normally don't mind TASVideos' resistance to change, but in this case, Niamek is proposing such a small, inconsequential, and easy-to-implement change that I think it's a pretty good idea.
I'd be interested in arguments against it from someone in addition to feos.
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GoddessMaria wrote:
So as for lately, I have been becoming more and more anxious and increasingly depressed... It also doesn't help matters that I might have had a hint of Autism either. I've constantly been a massive nuisance to everyone (even though unintentional) and lately finding myself thinking about just giving up and wanting to leave this world for Hell where I belong. Bad things always happened around me and it only will get worse... I feel far beyond broken nowadays. Life situations haven't improved much and "help" hasn't truly been good to me... I honestly am losing more faith and trust in everyone and everything... shutting off from the world on all sides.
...
Dark toned post, I know, but it conveys how I feel internally.
I'm sorry to hear that you're going through this hardship. I'd like to help you, but your post is fairly vague. Would you like to clarify it, possibly in a PM?
To the extent that you've included details, your post resonated with me quite a lot. I recently fell into a similar depression because I was underemployed, nothing seemed to be going right in my life, and a sudden breakup capped it all off and left me completely without energy. (If you PM me, I can talk about some other aspects as well.) I imagine our specific circumstances are quite different, but what you've written pretty much checks off all the boxes of how I'd been feeling: anxious, depressed, "hint of Autism", a nuisance...
I've never been suicidal in my life, but when this latest bout of depression hit, I had this overwhelming feeling of, "What's the point?" I still never seriously imagined taking my own life, rather I was just completely demoralized by what I saw as a long, inevitable downward trend for the future-- for me, my loved ones, and the world around me.
The good news is that just two days ago I secured another part-time job and I'm now "mostly employed". I've also been in regular contact with my ex-girlfriend and while we still have a lot to work out between us, I think that if I'm pulling my own weight, we might be able to patch things up with a lot of hard work and dedication.
I suppose the "bad news" is that misery loves company and as my mood lifts, it will be a little harder to empathize directly with you. I am still not out of the woods and I hope I can be someone you (or anyone) can vent to. I guess in a weird way I see you as not unlike myself two weeks ago, before I knew about this job opportunity. If I could go back in time, I'd say to myself something like, "Times are rough. You can feel bad and you don't even have to force yourself to work. Not everything is going to be fixed, but if you just hang in there a little bit longer, some aspects of your life are going to improve. While it won't be great, you'll be okay."
Since I can't go back in time, I'd like to say that to you.
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I share grassini's concerns. Since we're only hearing your side of things, we cannot possibly be sure what the "full picture" is or why you're getting the treatment you are. For emphasis, I don't think you're a bad person or necessarily antisocial, but there have been little hints throughout your posts, such as what grassini quoted, that suggest there may be a common thread of misconduct on your part.
I hesitated to bring it up because we can't know what your interactions with others are like and even if we did, no one here wants to kick you while you're down. The best I can say is that I also struggle with making horrible outbursts when I get excited and so I've done a lot over the years to put myself in an environment that minimizes those situations, actively dampen my own excitement, and reassuring myself that when I say something inappropriate, it isn't the end of the world. With that three-pronged attack, I've been able to rein in my outbursts or at least not let them weigh me down.
None of us can answer this for you, MUGG. If there's something there (and there may not be), I urge you to think very carefully about what you've said and how you've acted shortly before people turn on you. I'm not saying that to place the blame on you or justify their responses, but instead to make you feel empowered that this may be something you have some control over.
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I think that's outstanding advice overall, Warp. I wholeheartedly endorse everything you've said.
I'd especially like to reinforce what you've said about drugs and alcohol, however. Yes, many people are able to partake in them in moderation, but don't assume you will be like them. First, you never know how your body will react to an addictive substance and you can very easily find yourself dependent through no fault of your own except that you happen to have some "bad genes" that predispose you to addiction. And second, if you're already a lonely person, I think you're more likely to succumb to addiction as you displace your social life with your vices.
Those are just my two cents. I'm sure there's plenty of disagreement here, but frankly, I've seen far too many lives shattered by addiction, even to substances that we hold to be "socially acceptable".
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It turns out that water is not very viscous, so I'd ignore that factor. For example, a quick search indicates that milk is three times as viscous as water and while I doubt many people have tested this hypothesis, I imagine swimming through milk is not perceptibly more difficult than swimming through water. Furthermore, higher viscosity should help with your propulsion about as much as it would hinder you with drag. The effects should roughly cancel out and it should not be noticeably more difficult to swim through a somewhat more or less viscous substance.
As for density, I'm also skeptical of that as a standalone cause. The Dead Sea (saturated saltwater) is 24 percent more dense than pure water. Not only is this pool water likely not saturated, we would expect it to be easier to swim in more dense water, so we need to imagine some solute that decreases the density of the water. I didn't have much luck searching for such a substance (ethanol gets frequent mention, but there shouldn't be much ethanol in this pool water). Dissolved gas comes to mind, but since you said this pool is at a high altitude, there should be less gas in the water, not more. The density is directly affected by the ambient pressure and temperature, but another quick search indicates that it's affected by maybe one percent if you're talking about warm water at low pressure versus cold water at high pressure.
So in short, I'm doubling down on altitude being the chief factor here. I think that you experienced some mild altitude sickness that you were able to overlook in smaller pools at higher altitudes.
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MUGG, I do not have advice for your specific situation, but I can offer my heartfelt empathy. I am going through similar hardships in my life and I'd be happy to discuss that through PMs if you'd like. (I don't particularly want to discuss things here because I think it's a bit too much to unload at once and I don't want to draw people's attention away from others' problems.)
I think it's great that you're still fighting! (Your word, not mine.) As long as you still have the desire to better yourself, there's still hope. Since you've been vague about how you're fighting, I can't really weigh in with my thoughts, except I'll say in general that you may benefit from reflecting on what terms you're fighting these battles. For example, if you are responding to perceived slights by lashing out at people, that is almost certainly counterproductive. Again, without knowing specifics, I can't say anything beyond, "Think about how you're fighting."
One section of your post stuck out to me, however:
MUGG wrote:
Really, often when I walk through the city, I see there are just way too many people everywhere. The troubles and the meaning of one single person become so insignificant. I'm thinking they all probably live happy lives, while I'm walking here having to deal with these problems alone and still caged in my parents' home and my incapability to get my shit together. The thing is when you feel depressed or when you're alone, it becomes extremely difficult to do something. It makes me feel like I'm not important, after all I'm almost alone, so why even bother cleaning after myself, why even bother dealing with certain things, why even bother trying to go to a club and get to know new people (last time I tried that it wasn't a very good experience...)
This paragraph-- especially the part I've put in bold-- is the clearest indication to me that you are currently depressed, not simply falling back into depression. I don't know if there is a psychological term for this kind of state of mind, but to me, it is a textbook indication that someone is in a desperately depressive state. I think you should watch this video:
Link to video
All of it is good, but in particular, I'd like to draw your attention to the section beginning at 1:38, where he reflects on the people passing by who seem to be doing fine and thinks that no one cares about him. I've been through enough depressions myself and seen others go through similar episodes to recognize that depression goes hand-in-hand with the mindset, "Look at all these happy people around me who don't give a shit!" Part of me wonders if this might be a defining characteristic of depression.
Anyway, that is bullshit! I perceive that there are a tremendous number of people in the world who are, one the whole, simply unhappy. They don't necessarily wear their state of mind as a badge on their sleeve. Ask yourself if other people walking past you would recognized that you are a depressed or unhappy person. My guess is that they wouldn't be able to tell. If that's the case, why should you assume that the people you walk past are generally happy?
Western culture, for better or worse, has fostered an environment where it is very difficult to open up with others and admit that you are suffering. I think that's characterized our culture (Western European, North American, and East Asian) for centuries and is further exacerbated by social media such as Facebook, which exposes us to only the highlights of everyone else's lives while we are forced to live through the behind-the-scenes footage of our own lives. I don't think it's a coincidence that you are reaching out to us on a forum where you can remain anonymous rather than directly reaching out to your friends and family. (And if you are reaching out to your friends and family, I'd wager that they are unwilling to support you for the cultural reasons I outlined above.)
So I think that a sizable minority or perhaps even a majority of people out there are just unhappy in some way or another. That's unfortunate and comes with its own problems, yet I urge you to have the proper perspective when thinking about your lot in life. You're hurting, and even though a random passerby is unlikely to commiserate directly, they probably feel more like you than you would typically imagine them to.
I'll take this opportunity to get just a little bit preachy. There are too many people in the world. They are putting a strain on our natural resources, our economies are rapidly shifting away from manufacturing and development and towards services and bureaucracy, leaving us feeling unfulfilled, and our political representation is being strained by high populations. I don't have any silver bullet solutions for the big-picture problems that lie ahead, but I urge everyone to not pass on the pain. Do not bring children into this world if they are likely to lead miserable lives. I think it would be good if most people had zero children (not even one), but for a more practical solution, I encourage everyone reading this to think about the number of children you would like to have and then subtract one from that number. Reduce the strain on our resources and stop the chain of misery.
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My first hypothesis is that altitude is a factor. Is this country club at a very high (or perhaps low) altitude? I'm not sure exactly how that would affect things, but I can offer a few theories. It would decrease the amount of gas dissolved in the water, affect your stamina, and it would change your own density as you attempt to float.
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I also did this problem but waited to see if anyone else wanted to chime in first. Like NxCy, I recognized that this is a (slightly underdetermined) system of simultaneous equations. I chose to use the substitution method. I've pasted my work below; dashed lines indicate a substitution has taken place while blank lines separate equations that already have an isolated variable:
B=2A
C=2B
Y=B+X
Z=A+B+X
X+Y=B+Z
D=A+Z
---
C=4A
Y=2A+X
Z=3A+X
X+Y=2A+Z
D=A+Z
---
Z=A+Y
2Y=4A+Z
---
Y=5A
Z=6A
D=7A
C=4A
X=3A
B=2A
So I agree with NxCy.
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Warp wrote:
I suppose that any sequence can be made "slower" by making a variation of it with more terms (such as, for example, and I suppose, in the Leibniz formula rather than using odd numbers directly, make each term a sequence that converges to said odd number, or something), but I suppose that the spirit of my question was not really "can you take an existing formula and create a variant of it that has more terms". Rather, if there's a completely different unrelated formula that's slower. (Although, I suppose, "unrelated" may be too fuzzy of a requirement because many sequences approaching a given value can be converted into each other by applying some transformations.)
It's hard to make abstract ideas unambiguous, when dealing with mathematics.
Huh. That's actually kind of interesting to me and I'd like to look into it but I'm a little busy. Let me try to formalize this.
Let a_n be a sequence whose corresponding series converges to A at some rate O(f(n)).
Let b_n be a sequence whose corresponding series converges to 1 at some rate O(g(n)). (It could converge to anything, but for the sake of simplicity, let's just normalize it so that it converges to 1.)
Define a new sequence a'_n to be such that
a'_0 = a_0*b_0
a'_1 = a_0*b_1
a'_2 = a_1*b_0
a'_3 = a_0*b_2
a'_4 = a_1*b_1
a'_5 = a_2*b_0
...
and so on. I'm not quite sure how to write this in closed form, but the basic pattern is that for every k, a_i*b_(k-i) is represented consecutively.
This new series, a', surely converges to A because each of the terms a_n is represented as a series in b_n. At what rate does a' converge to A?
Edit: Some random musings on the above problem: I wanted to throw out a guess as to what the rate of convergence should be, but nothing is coming to me. The one thing that I'm comfortable guessing is that the rate may be divided by n^2, since the size of the partitions increases as n^2. The bigger piece, however, is the interplay of f and g. As g increases, the rate of convergence should also increase, but it is not at all obvious how. Do we take f(n)*g(n) or perhaps one of the composite functions, f(g(n)) or g(f(n))? No, none of those make sense because they allow for a series split in this way to converge faster than our original series. I guess I also see an issue with attempting to order the rate of convergence. We would intuitively take O(exp(n)) to be faster than O(n^a), which is still faster than O(log(n)) for a few examples. But what about O(1)? That is a trivial series that converges after a finite number of terms. For example, we could have b_0 = 1 and b_k = 0 for k>0, giving us the fastest possible convergence. Does O(1) break the intuitive pattern I've outlined above?
These thoughts lead me to believe that this problem may be ill-posed.
Edit 2: Upon yet further reflection, I've realized I don't really know how to properly apply big-O notation to series convergence. I'll need to reformulate the question. I'm still busy, though.
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I don't think this is as bad an idea as others have suggested, especially if it's another tier. Having said that, I feel pretty conflicted about the idea. Basically, I see it as having very little upside or downside. I think it would, on some level, be nice to have a comprehensive list of the fastest completion times for every game, regardless of level of optimization. For certain games, such as Super Mario Bros. (pretending it hasn't been TASed to death), this is a kind of stupid idea. There are simple optimizations to be made and anything less than that is just pure laziness. On the other hand, I could see a place for this tier with games like Tetris, which are heavily RNG dependent and for which perfection is often the enemy of good enough.
On top of that, however, you have issues of the extra workload for judges and a rush to produce as many runs of crap games as possible. This tier would probably need to be constructed such that it is divorced from our point system and has stricter standards on what games are allowed.
I vote "meh" on the idea. I wouldn't be against it but I'm not clamoring for it either.
Experienced Forum User, Published Author, Player
(79)
Joined: 8/5/2007
Posts: 865
thatguy wrote:
The monkey is very clever, and knows the vendor leaves his market stall unattended for a few minutes at the same time every day to pray, leaving a partially full box of bananas.
As I'm familiar with this problem, I'll point out that the amount of bananas in the box is uniformly distributed on the interval [empty, full].
Put in more mathy terms, let f(x) be a uniform probability distribution function on the interval [0,1]. That is, f(x) = 1 if 0<x<1 and f(x) = 0 elsewhere. Values are selected from this pdf until their sum exceeds 1. Let the number of selections be N. Show that on expected value of N is e.
I've never actually tried to prove this. I'm going to guess that one way it can be done is with the convolution.