Firstly, i must apologize for not reading through all of that. (it's kinda early and i am a very lazy person) Regardless, the little i did read, along with some quick thinking, has led me to the conclusion that you are, in fact, correct, and i was a fool for not seeing that after your first post. (Yes, i did take Algebra, but considering my laziness, i decided to rely on simple logic instead, but wasn't careful enough and made a stupid mistake) Indeed, your explanation makes sense (i did skim it, just didn't read each and every word). My basic mistake was just multiplying the numbers together instead of raising one to the power of the other, as you pointed out. (i hate myself for that, it really was stupid) So basically, we need to multiply all the possibilities for each block together with those of all the other blocks. Meaning (324*324*324*...*324) - 300*300*255 times. Which does indeed lead to 324^(300*300*255). I am not sure what you were doing when you got the 2^(300*300*255) thing (you are complicating the matter by just including 2 blocks at first. This may be for clarity and explanation, but it makes the end calculations more confusing, i think), but i am pretty sure, 324^(300*300*255) is the correct (and precise, for that matter) result. So, um... yeah. Now we have got quite a few posts filled with mathematical jargon (not sure if a good or a bad thing), which could have been avoided, had i been more careful. Oh well. Nonetheless, i must admit, i found this to be indeed quiet fun. Maybe we'll do one of these again some time, who knows? Yes, i know laziness is not a valid excuse for anything, but it's all i got. So i abuse it. You can hate me for it, if you want.
First off, sorry for kinda sorta hijacking the thread (I guess?) and yes I forgot to raise the number of blocks, to the number of space we have, so in other words 324^(300x300x256) which gives us... Well damn I can't calculate that, the biggest number I could calcute, is 324^99999, which is nowhere near close enough, but we'll do some extremely rough estimates either way. which gives us 978 x 10^7752, or in other words, 978 followed by 7752 zeroes. let's say for a rought estimate, this is 999 x 10^8000, but wait this is only 324^99999, but we need 324^23040000, so let's say (estimate again, now I'm talking about the estimate for 324^23040000 btw) that we have 999 x 10^99999 on our hands, that's 999, followed by 99999 zeroes (I know I'm probably under/overshooting the actual number by several decimals) Now, let's convert that to years, or even better milleniums (if you do 60x60x24x365x100 you only get 3.1536x10^10) now we divide 999 by 3.1536 and subtract 99999 with 10, so 316.7808219x10^99989 years or. 3167808219 followed by 9982 zeroes.... yeah. It would take that many millenia if each calculation takes 1 second, but let's not stop there. Divide this by 1000, and you get 31x10^9980, that's in milions of years, divide by 1000 again 31x10^9977, that's in billions of years, we can keep doing this really 31x10^9945 decillion... yeah that's a big number... (perhaps you could say 310 decillion decillion decillion x9945 but that's not how you should say numbers) Also after rereading this, we forgot all orientations of torches, stairs, etc) But I think this is a fairly good estimate. I used https://defuse.ca/big-number-calculator.htm to calculate 324^99999 btw just so you can see how big that is. To get back to the reason this thread was created. I think Athion is a server full of people who like maths (but only if they involve very big numbers of course.
So the server still isn't up? I'm so bored... Why did Pwego have to go down before the new server comes online?
324^23040000 is the first term in a huge polynomial that actually represents the true number of arrangements of 324 physical blocks within a 300*300*256 spaces. The huge polynomial being (x^23040000 * 1^0) + (23040000x^23039999 * 1^1) + ... + (x^1 * 1^23039999) + (x^0 * 1^23040000) x=324 (not 325) All of the terms with 1^(number) can be treated as 1, since 1 to any power is simply 1. That huge polynomial is equivalent to (324 + 1)^23040000 which is simply 325^23040000, NOT 324^23040000 Had you read my proof, you would understand that the true number is 325^23040000 I redid the proof treating the air block as a physical block rather than a non block (much faster method btw), and I got the same number: 325^23040000 Just so you know, 325^32040000 is WAY WAY WAY larger than 324^23040000 (trust me on this one) Unless you already factored in the air block into the 324 block. I hope you guys didn't -o- I would like you guys to note that 325^32040000 is a very very very tiny number in comparison to some of the other numbers higher level mathematicians have conjured up. :)
Funny thing is happening here... we contradict each other but it would appear that we mean the same thing. Quoting the part of your proof i think you were referring to: Yes, i did read it. And i agree with it. But, and you mentioned this as well, considering air an actual block makes the entire thing way less complicated. The above quoted snippet of your proof relies on working with a notion of 'nothing', or 0. The difference in our results can be traced back to this fact, because, using this method, you add one 'block' (not in the physical sense, since it's actually nothing, but in a mathematical sense). But in my calculation, i already included that 'nothingness', represented by air. And that leads us right to your question. Yes, we did factor in air as an actual block. At least that's what i assumed after reading Joules' initial post. (i did not count the blocks myself, so i do not know for certain, if 324 is indeed the accurate number. But i was basing my arguments on the assumption that it is) So, this is what (i think) we can agree upon: We came to the conclusion that the number of possible arrangements of 324 blocks (including air) inside a 300x300x255 space is 324^(300*300*255). If we assume the number of blocks is 324, excluding air, then the final answer changes to 325^(300*300*255), since we do include an additional 'block' in the calculation, in the form of 'nothing' or 0, if you will, thus increasing the number of 'blocks' to 325. You mean things like Graham's number? Um... yeah. Way to big for my silly little brain to comprehend.
If you think about realistic minecraft you can't put in the extra block that is nothing because in minecraft terms the air block is nothing, in other terms air is the place holder (if you know what i mean) So you can't have "nothing" becuase "nothing" is already in the equation as air
But it still contributes to the number of arrangements @Reuben @noskill11 NOOOOO!!! WHY DIDN'T YOU TELL ME THAT AIR WAS ALREADY INCLUDED!!! D: I'VE WASTED ALL OF THAT TIME!!! D: Well at least it was good AMC practice! xD Glad to have had this conversation.
Yeah air is factored into the 324, I think I mentioned this in my first post (in which my calculations were horribly wrong of course) edit: did I forget to mention that all orientations of torches, levers, stairs, logs and buttons are NOT factored into that 324? Cause visually atleast that changes up the look of that 300x300x256 space quite a bit.
Guys, I think it's safe to say: This math is beyond mortal comprehension; we should leave it to the likes of gods that are the owners of Athion, and the creators of Minecraft.
3x-3 is 12. X is a variable. If there is nothing between 2 numbers, that makes it a (times). So lets say x is 5. 3 times 5 - 3 = =15 - 3= =12