ee mathamatics

Master1 · Before February 2015

Squad wrote:

Master1 wrote:
It is impossible to figure out because of this!!
Fdoou wrote:
a smiley spawns in the bottom of a great world in the exact center
You cannot spawn in the exact center of a great world. Great worlds are 398 long (excluding the borders). Since this is an even number, you would have to spawn perfectly between 2 blocks. You can't do that !

Blocks are 16px wide so you can spawn with 8px on one block and 8px on the other, it is completely possible.

put a spawn point only fits on one block, you can't place it between blocks !

Koya · Before February 2015

Master1 wrote:

Squad wrote:
Master1 wrote:
It is impossible to figure out because of this!!

You cannot spawn in the exact center of a great world. Great worlds are 398 long (excluding the borders). Since this is an even number, you would have to spawn perfectly between 2 blocks. You can't do that !

Blocks are 16px wide so you can spawn with 8px on one block and 8px on the other, it is completely possible.
put a spawn point only fits on one block, you can't place it between blocks !

Ok, that's what you meant.

Bimps · Before February 2015

i found how you screwed up this topic. delete {center} and {/center} in the part where you have the images of the world.

Last edited by Bimps (Jul 28 2014 3:48:35 pm)

Koya · Before February 2015

Bimps wrote:

i found how you screwed up this topic. delete {center} and {/center} in the part where you have the images of the world.

I just removed all of the quotes.

Tako · Before February 2015

Squad wrote:

Bimps wrote:
i found how you screwed up this topic. delete {center} and {/center} in the part where you have the images of the world.
I just removed all of the quotes.

Back on topic.

Tako · Before February 2015

Creature wrote:

ewoke wrote:
> blocks in the world are randomly arranged
so its not 0.01375%
But it's the minimum to be used.

0.000838% (8.38e-4%) is the hypothetical minimum, or in other words, 66 blocks out of 78 804.

It is possible for the 66 blocks to be randomly generated in a column that lets you leap frog your way to the top. 66 is the minimum number of blocks to accomplish that task.

The odds of that happening are roughly (398 * 19^65)/(8e4^66), but my point stands. It's possible, and therefore should be considered the least % density required.

More accurately, since the bot cannot place where there are already blocks, it becomes this:

(Explained here)

Bimps · Before February 2015

<snip>

Last edited by Tako (Jul 28 2014 4:42:54 pm)

Fdoou · Before February 2015

Master1 wrote:

It is impossible to figure out because of this!!
You cannot spawn in the exact center of a great world. Great worlds are 398 long (excluding the borders). Since this is an even number, you would have to spawn perfectly between 2 blocks. You can't do that !

i dont think you understand how math work

@muftwin: read the question or leave
@all: what is the maximum % of blocks that can be placed before the level will never be solvable? i believe it requires 263 empty spaces, which i believe is 99.67125% of the blocks filled.

Last edited by Fdoou (Jul 28 2014 6:27:06 pm)

hummerz5 · Before February 2015

You say that you don't expect an answer
and yet you ask.

imo, the best percentage won't help you. Considering how getting to that # won't actually guarantee a possible world, I'd try and have a bot attempt to complete a path through after each block.
Good luck making that.

But otherwise, this number, in practice, isn't helpful.

Tako · Before February 2015

Moved to Q&A.

Fdoou · Before February 2015

hummerz5 wrote:

You say that you don't expect an answer
and yet you ask.
imo, the best percentage won't help you. Considering how getting to that # won't actually guarantee a possible world, I'd try and have a bot attempt to complete a path through after each block.
Good luck making that.
But otherwise, this number, in practice, isn't helpful.

i know this requires a supercomputer to properly solve, but i'd like to see how close we could get before that.
i don't really know what your problem is, so he re is a wikipedia art icle on the purpose of this topic

hummerz5 · Before February 2015

Interesting. You consider this fun.

good to know.

Fdoou · Before February 2015

math and solving problems like this is tons of fun
not sure why you are so cynical

Tako · Before February 2015

Some people have wartime flashbacks when they hear the word "math" or "problem solving" because most teachers don't bother with curiosity, they just shove it down your throat. And some are bad at even that. After an experience like that, you don't care about math, you won't want to see math, and you certainly don't want to like math.

However, once you obtain a little curiosity in the vast world of mathematics, stuff like this becomes enjoyable, and you end up studying it by yourself. And you need to study it by yourself if you're in public school.

Also nobody commented on my fancy equation

Fdoou · Before February 2015

your fancy equation was nice, but i just don`t have the education to understand what it means yet

Tako · Before February 2015

It's not all that hard to understand. I'll explain it because I like explaining things and math is enjoyable to explain. (I'm studying to become a teacher, too. Good practice.)

Probability is calculated like

And if we want to find the probability of two separate things happening, we multiply them. That's just Algebra I. The fancy capital pi just shortens what would be a 66-term denominator. Ain't nobody got time to write a denominator with 66 terms.

----
The first probability is that the block will be placed anywhere on the line Y=296. There are 400 blocks on that line, but the bot can't place on the border, so the number of successes is actually 398.

The number of possible blocks is (400*200) minus the sides, which is (2*400 + 2*200 - 4). That means there are 78804 empty blocks in a great world.

Here is the equation for the probability thusfar:

----
The second probability is that a block will be placed exactly 3 spaces above the previous block. It must also be in reachable distance.

In other words, one of the gray or blue blocks from this image:

There are exactly 19 blocks that satisfy these requirements. The total is still 78804, but since the bot can't place where there is already a block, it's 78804 - 1.

So now we multiply the new probability times the first one:

---
The third probability is almost exactly the same as the second probability. There are exactly 19 number of successes. Except this time, there are two blocks placed in the world. So the total is 78804 - 2.

The new equation:

---
Repeat until we reach the top, which is 198 / 3, or exactly 66 times.

Nobody has the time to punch that into a calculator. Since it is a pattern, mathematicians could invent short way to do it. And they did, it's called pi notation. It works like this:

"[max]" is the maximum number. In our case, 65. [start] is the number it starts at. In our case, 1. x^i represents an expression that uses the variable i. (note: i in this scenario does not stand for "imaginary", it stands for "index")

What a calculator will do is start at i=1, and then
• evaluate the term with the value of i
• multiply the answer with the previous answer
      • Note: the only difference between sigma notation and pi notation is that sigma adds, pi multiplies.
• Add 1 to i
• Check if i > 65.
      • If it is, it's done.
      • Otherwise, repeat.

So now, instead of a term with 66 terms in the denominator, we change it to pi notation and end up with something that is very short and easier to calculate:

Alternatively, you can multiply the numerators since they are constant, and move the pi expression to the denominator. When you do that, the pi expression changes to incorporate the first denominator.

They both mean the same thing. The second one's just more condense and less intimidating.

The point of this entire post is to explain how it is possible to use 0.000838% density and get to the top. It's just super rare.

[Edit] Thanks to the guys at math.stackexchange / Wolfram, the probability is approximately 4.5954×10^?241 %

Fdoou · Before February 2015

wow its like reading a textbook that is your friend

hummerz5 · Before February 2015

I have yet to take a curiosity to mathematics. Thanks, though, for the explanation of pi notation.

I'm still of the opinion that the mystery number posed by the OP is not of use.

But now we know the bottom.

Fdoou · Before February 2015

why does it need a purpose

Anch · Before February 2015

I'm the only guy here that doesn't understand the op?

Fdoou · Before February 2015

no, some man, creature, and the others obviously didn't either

Tako · Before February 2015

More math, just for fun.

4.5954×10^?241 %

If we invert the probability, we can get the approximate amount of tries it would take in order to get it.

The percent is probability * 100, so just add 2 to the exponent of the percent.

4.5954×10^?243 %

Invert it using a calculator and we get

2.1760×10^242

A little less than two and a half googols. Nothing that a bot can't do, right? Bots are super fast.

Well, each of those attempts represents sending 66 blocks, followed by a check, and then a clear. Let's run on the quicker side and say that it takes 300 milliseconds. (Too fast and you will overwhelm the server or your computer)

2.1760×10^242 * 300 milliseconds

But nobody cares about milliseconds. I have a hunch this is going to take a couple years, so let's convert this more.

(2.1760×10^242 * 300 milliseconds) / 1000 (ms per second) / 60 (second per minute) / 60 (minute per hour) / 24 (hour per day) / 365 (day per year)

2.0700×10^234 years

The entire age of the universe (13.798×10^9) doesn't even scratch how long this would take.

A year for every atom in the universe isn't even the square root of this. You would have to cube the number of atoms in the universe to even come close.

thecoolguy · Before February 2015

Tako dont you need 65 blocks? You also have a jumping height and you start 2 from the bottom

Tako · Before February 2015

thecoolguy wrote:

Tako dont you need 65 blocks? You also have a jumping height and you start 2 from the bottom

Uh... yeah... I was just testing you guys to see who actually read it.

Bimps · Before February 2015

so ee is more complex then the universe?

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