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PostPosted: Fri Oct 01, 2004 11:42 pm 
PPT Toddler
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Oppolo wrote:
Remember to consider that marbles are round, so they'd sink into each other a little bit. To get it to the maximum height (as it's asking for the maximum height they can get), you'd make the sides of the marbles touch- and then rest the others ontop. It'd indent a little, but not much- you could probably do it with a diagram... pretty hard to do, I'd say, but it's definately a factor.


If we count with them sinking into each other, then we would have to multiply every layer with irrational number of centimeters, wouldn't we? Because we don't know how perfectly they sink. So I just considered the marbles as cubes.


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 Post subject: so far
PostPosted: Fri Oct 01, 2004 11:55 pm 
Beyond Godly
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what I got so far..

1050311*2=2100622 marbles


So starting from the top in a three sided picture like thus

Image

P total per tier and = total altogether
1~1
12~3 =4
123~6 =10
1234~ 10 =20
12345~15=35
123456~21=56

1+2+3+4+5+6=21+35=56

Now, is there an easier way to do this?


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PostPosted: Sat Oct 02, 2004 12:07 am 
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This is what I did.

----
starting
----

rows = 0
kikos = 1050311
in the rows = 0
kikos*2

the number of marbles in # of rows+1:
rows+in the rows
--------
repeat many times, then
--------

rows*2

thats how I did it


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PostPosted: Sat Oct 02, 2004 12:44 am 
Beyond Godly
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My brother, my friend and I got an answer. But the number of marbles doesn't work out to an even number of rows -- you either have marbles left over or you're short some (and that goes for both numbers of kikos, released and actually created).

I entered the answer for how many rows they could make if they built it to a point of 1 marble and then had some left over. Now I realize the question was phrased "how high can the pyramid get," which means it doesn't necessarily have to end in a perfect point of 1. It's probably how high they can build it before they run out of marbles.


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PostPosted: Sat Oct 02, 2004 12:55 am 
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Im totally at a loss here. Can anyone pm me their strategy in child term's? I'm feeling blonde :)


:( but my siggy and avatar were brandon boyd!


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PostPosted: Sat Oct 02, 2004 12:57 am 
Beyond Godly
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Dude, I don't even understand it. It requires two different math formulas. I got someone with a math degree to help me out. ;)


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PostPosted: Sat Oct 02, 2004 1:26 am 
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Cranberry wrote:
Dude, I don't even understand it. It requires two different math formulas. I got someone with a math degree to help me out. ;)


I've got a friend whos an accountant... I'll go ask him if he can figure it out.

EDIT: That is, if I can ever get Neopets to load...


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Set by WIS (I think XD), awesome fader by Bangel!


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PostPosted: Sat Oct 02, 2004 1:44 am 
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Well, they don't expect it to have no leftover marbles. It is the most rows you can make with the marbles available. It should be close to 250-300, I think. I think the safest way to do it would've been to write it all out manually so you can see all the results.


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PostPosted: Sat Oct 02, 2004 2:15 am 
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with my dad's help, we put together a spreadsheet in Excel to figure it out.
From what we figured out, it does come up short, so not all of the marbles are used.

The answer, as far as we can tell is:

guess (Warning: do not put your mouse over the link or click the link if you don't want to know the answer.) (remember - there is no ".", the "." is only there to make it a url - a space should be in its place. such as: x cm, not x.cm)


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PostPosted: Sat Oct 02, 2004 2:19 am 
Beyond Godly
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I didn't get a number that high. The one I submitted was between 200 and 300 cm... but I think the real answer (the one my friend submitted after we realized the pyramid probably doesn't end in a perfect point) is between 300 and 400 cm.


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PostPosted: Sat Oct 02, 2004 2:32 am 
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i found a system that is hard to explain. but if your answer was 200 then you only used 20,100 marbles. and if you put 300 you only used 45,150 marbles.

Correction: Using the method said earlier by another user I found that by level 87=3828marbles=113,574marbles total.

I already have the avatar and bronze trophy so i decided to not try any method's and do this one by hand. it will take me a day but i will get the right answer. for everyone. :)


:( but my siggy and avatar were brandon boyd!


Last edited by artemisanoush on Sat Oct 02, 2004 4:32 am, edited 1 time in total.

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PostPosted: Sat Oct 02, 2004 2:33 am 
Beyond Godly
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I think Neopets has actually used the max amount of kikos instead of the current. So there would be 1050000 kikos


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PostPosted: Sat Oct 02, 2004 3:23 am 
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artemisanoush wrote:
i found a system that is hard to explain. but if your answer was 200 then you only used 20,100 marbles. and if you put 300 you only used 45,150 marbles.


How can that be? If you used 200 layers the base layer alone would have 39601 (199x199).


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PostPosted: Sat Oct 02, 2004 3:52 am 
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yptee wrote:
Oppolo wrote:
Remember to consider that marbles are round, so they'd sink into each other a little bit.


The question actually said height of each level is 2 cm, so this is irrelevant. I got an answer betweeen 400-500 cm too.


I agree with yptee, the sinking is need not be taken into consideration. And I got a similar range of answer to him.

Hint:
If there are 4 rows, total number of marbles should be 1 + (1+2) + (1+2+3) + (1+2+3+4).

Objective is to find the number of rows, but u gotta use number of marbles to help u.

Eg, if there are only 10 kikos, there are 20 marbles, that means they can only stack up to 4 rows, meaning it would be 4 x 2 = 8 cm high

I tried to solve it by using a double summation at first, summation of the first n terms followed by the summation of that result from 1 to m. In other words, a summation (from 1 to m) of the summation of the first n terms. This answer must be less than or equal to the number of (kikos x 2). From there, solve the cubic equation and find the nearest integer m that satisfies the inequality.

Haha... Anyone even understand what I'm saying? Graduated with a degree in maths, but honest, u don't really need university knowledge of maths to do this. High School is enough.

On a last note, I tried using summation as mentioned earlier, but I couldn't solve the cubic equation because the number was too big. Neither did I use any maths algebraic software to help me with it. I simply took the advice of one of the hints earlier to help me out.


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PostPosted: Sat Oct 02, 2004 4:42 am 
Beyond Godly
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genie_mcbeal wrote:
I simply took the advice of one of the hints earlier to help me out.


Which bit of advice, I MUST ask :)


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