NeoPets Riddles (Lenny Conundrums) and Answers Here

I'm getting 7252 litres

EDIT: Method

Each block is .97 by .97 by .63 meters. This means that exposed sides are .6111 m^2 and tops are .9409 m^2

Given a layer made up of n x n blocks, each side of it has n faces exposed, for a total of 4n. To get the total number of exposed side faces, add them all up: Sum(n,100,1,4n) = 4 x Sum(n,100,1,n) = 4 x 100 x 101 x .5 = 20200. This means a surface area of 20200 x .6111 = 12344.22 m^2.

We can't forget about the tops, however. The thing to notice is that you can flatten the exposed areas of the tops of all the layers and get the total area of the bottom layer. So 100^2 x .9409 = 9409 m^2

12344.22 + 9409 = 21753.22 m^3
21753.22/3 = 7251.07333 liters, round up to 7252.

Good luck to everyone.

Here's what I did:

First, I found the surface area of the sides of the cubes. For each layer, there are four sides of the pyramid, each showing one side of a cube times the number of cubes on a side.

To easily count this up, I first found how much surface area of one of the four sides of a pyramid has. (Just the sides of the cubes, not the tops).

There are 100 by 100 cubes on the base, and it down to 99 by 99, 98 by 98, all the way down to 1 by 1. So to count the cubes, you would have to add an entire sequence.

100
+99
+98
+97
+...
+1

I decided to take a short cut and did the following:

1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
...
50 + 51 = 101

So counting up from 1 to 50, we can match a number to add up to 101. So the number is simply 101*50, or 5050.

5050 is the number of blocks that we count the side surface area for on one side, but there are for sides to a pyramid. So the total rectangles we paint on the side of a cube is:

5050 cubes per side * 4 sides = 20200 cube faces.


We want our answer at the end to be in Meters instead of Centimeters, so we convert before multiplying. The surface area of a side of a cube is:

97 cm * 63 cm = .97 m * .63 m = .6111 m^2

That's the surface area of just one cube. The surface area of all the cubes is:

.6111 m^2 per cube * 20200 cubes = 12,344.22m^2

12,344.2m^2 is only the surface area of the side of the cubes. We still have to find the surface area of the top of the cubes. Now this part may seem tricky until you find a little secret to getting around it.

The pyramid is centered, so the way you find the surface area of the blocks shown on each level is to take the total area of that entire level and subtract the total area of the level above it.

We end up getting this:


(100 cubes * 100 cubes) - (99 cubes * 99 cubes)

+

(99 cubes * 99 cubes) - (98 cubes * 98 cubes)

+

(98 cubes * 98 cubes) - (97 cubes * 98 cubes)

+

...

+

(2 cubes * 2 cubes) - (1 cube * 1 cube)

+

(1 cube * 1 cube) - (0 cubes * 0 cubes)


As you see, each level, the new term you are adding is the same as the term you just subtracted, therefor the entire surface area of the cubes is just the area of the top of the blocks on the bottom of the base (100 cubes * 100 cubes).

Another way to realize this is to look at the cube from the top looking straight down. If you had no depth perception, you would just think that you were looking at a 100 cube by 100 cube square with smaller square designs carved into it.

So the total surface area for the top of the cubes is:

(100 cubes by 100 cubes) * (.97 m * .97m)

=

(10,000 cube faces) * (.9409m^2)

=

9409 m^2



Now, we add our two surface areas to find how many total square meters we have.

12,344.22 m^2 + 9,409 m^2 = 21,753.22 m^2

If one litter can cover three square meters:

21,753.22 m^2 * (1 litter / 3 m^2)

=

(21,753.22) / 3

=

7251.07333... litters.

They ask us to round up to the nearest litter, so the final answer is 7,252 litters.

Just found this forum, could be handy

I managed to get that as well, using the same thinking hope it is correct

Although I did get Excel to make sure the maths was correct!

That said, having had a go at a few of the riddles I do think I prefer the more mathamatical ones!

Indeed, the other ones are questional.

No one knows why the Flotsam wasn't in the lineup, yet the answer was still Taelie...

And before that, you had to guess how many were hidden.

Personally, I said "Neopets likes round numbers... 40..." so I got the prize that time, even if I'm still trying to get the Avie.

This time, though, I think I managed to submit it fast enough. I found the answer, submitted it, then typed up the solution here before much else could be posted.

Hopefully that means I beat all the people who just find the answer on this site then get it.

x, you may have had the answer posted before I did, but I managed to type up my lengthy solution before you.

Isfan,

It doesn't actually say that the pyramid's centered. The result holds as long as each layer doesn't extend past the one below it. All the layers could be pushed up against one edge and the answer would stay the same. Kind of stupid to point it out when it doesn't make a difference, but the logician in me couldn't resist Anyway, I'm a slow typist


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The LAST LC
I think the reason the flotsam was not listed is because the riddle never stated the pets were listed in consecutive order just in order. If they were consecutive then the flotsam would have had to be listed. Yes another trick by tnt.

Come on, X, this is Neopets. I know that the Pryamid doesn't have to be centered, in fact the way I first convinced myself was by pushing all the layers to have a uniform corner.

But this is Neopets we're talking about, and the desert. The pyramids in the desert are always centered.

I only mentioned it being centered because a lot of people may look at that part of it and think they have to do a lot of hard work, and I just wanted to disprove that.

When I put into my solution that the pyramid was centered, that was just so that people knew they didn't have to go off and do any lengthy calculations. Before I saw the shortcut, I had the .97 length divided in two and was trying to calculate the bottom layer to find an equation to quickly add up all the exsisting layers until it hit me and I went "Duh!"

And I think I had the answer first too, because when I went to type up my solution I didn't see your one line "I'm getting 7252 litres." message yet.

Re: The LAST LC


What I don't like is that that trick could have gone either way.

Neopets could have sat there laughing and said "Haha, it was a trick. We just didn't mention it."

OR

Neopets could have sat there laughing and said "Haha, it was a trick. The flotsam wasn't there, and neither were [insert other people for some odd TNT reason]."

Re: The LAST LC
Agreed. Why should we assume the rest are consecutive if the first few weren't without a good reason.

Re: The LAST LC


Eh, but what are we going to do? Start a petition to get Fyora as a second acceptable answer? There are about 1-2 thousand winners a week, so I think it'd be a bit hard for us to find 10 thousand people to sign it. Besides, I'm sure they already lost who sent in what wrong answers. It's unneeded data, why keep it?

New Connumdrum is out:

---------------------------
With all of these ancient scrolls being discovered around the Lost Desert, the city of Sakhmet needs to build a place to store them all and keep them safe! It has been determined by city engineers and architects that a huge stone pyramid, painted gold, would be a fitting storehouse for such treasures of knowledge!

The base of the pyramid is 100 blocks by 100 blocks; each successive layer is one less block wide and deep, until the top layer which is simply one block. Each block is 97 cm wide by 97 cm deep by 63 cm tall.

If one liter of paint can coat exactly three square meters, how many liters are required to coat the entire exposed surface of the pyramid? Round up to the nearest liter.
----------------------------------------------------

Ok so i used a excell sheet to do this one. This is my reasonning:

First calculate the surface of the lateral sides of each layer.
#blocks*97*67

That multiplied by 4 gives you the exposed lateral surface on ONE layer.

Next calculate the exposed top surface of each layer. So the top layer surface is given by
(#blocks*97)*(#blocks*97)
To know the exposed area, you must substrack the top layer surface from the layer above it.

After, add up all lateral and exposed top layers, divide by 100 (to get meters). You'll get the total exposed surface of the pyramid.

Divide that by 3, round up and you will get the answer.

The correct solution has been posted twice already. Both of those posters recognized that you don't have to calculate the top surface area for each layer.

This is where stapel comes in and displays the answer in a big red font.

Hi, I am a complete newbie to message boards and posting, and not even sure if i'm writing this to the person who originally posted the above quote or so that everyone can see it. (sorry for wasted space) But I wanted to know how you know they said they would accept 2 answers? is it something you can read on the neopet site or is it information you got from another site? I mostly want to know because i put fyora as my answer, and i think she was the correct one wasn't she? But I didn't get anything at all. could i have been to late in submitting my answer to even be counted?

thanks

semi confused

It was Taelia not fyora

I got 7252 liters. *falls down dead after fingers fall off from typing lots of numbers*

so like,,whats the answer??
i tried ALL i could to find it out,,but heck,,im only 11,,so how would i know??
lol

This was in response to Round 119, where there were two possible answers, since the question was "How many Neopoints would you need to buy one of everything in the Hidden Tower?" That week, the price of the Supreme Faerie Queen Doll dropped for Fyora Day only, then went back to the normal price, so it's unfair to accept only one answer and not the other. For every other conundrum, there SHOULD be only one answer they're looking for. The last one, their answer was Taelia, so your answer was counted wrong.

My friend's brother ended up with an answer in the 600,000s
He won't tell me what his results were.
I'm not exactly sure if he's right or not.
I'm going to keep scribbling down some equations until I find an answer that looks probable.