NeoPets Riddles (Lenny Conundrums) and Answers Here

i got it!!! Thank you for the hints, Kutusita. Haha. Some one else help me more. Hint: First word, right column. I doubt anyone would know, anyways. Haha. It goes up in an odd number. It is non-linear, the way it goes up. So there. Your hints. you have a day. Good luck.. ;DD

I guess I'm extremely stupid because I still have no idea.

Nevermind. I found the answer somewhere else. I don't know how people figured this one out. It's insane.

The answer is out. It's balthazar.

Here's how I solved it: I looked up 'site:www.neopets.com outsmart' in Google. In the middle of the second page, there was a link to an old Neopian Times page. (Currently, it is the first link that appears when you search, thanks to this puzzle!) That page did not show me the word (or showed it in an awkward position), but then I clicked "The Neopian Times Week 81" (Week 81 link also worked). I then saw that "Outsmart" was the first word in the second column. "Outsmart" was the 9th word in the sequence, and the issue number was 81, so the issue number was the word's place in the sequence squared.

The sad thing is that I was looking at old NTs in week 1, but was going in the wrong direction. I looked up 371 (LC number) in Wikipedia, and it had two interesting facts: one, 371 is an Armstrong number (i.e, is 3 cubed plus 7 cubed plus 1 cubed is 371), and two, it is made up of consecutive prime numbers, starting with 41. So, I was looking at prime number editions instead of square editions. If only I had pursued looking at them more methodically, starting at 1!

I also looked at Kreludor in case Armstrong was a reference to Neil Armstrong.

r the first 250 correct entries is a Water Faerie Water Blaster. You will also get a cool trophy that people can see when they do a user lookup on you! And all correct entries will split the 2,000,000 Neopoint prize pool.

THIS WEEKS PUZZLE - ends Next Wednesday, most likely
Moltara is a very hot place, and the demand for cold water has been increasing ever since more people started to visit. Therefore, the people of Moltara decided to build a new water tank.

This water tank is a perfect sphere with an inner radius of 12 metres. However, they used inferior materials to build the water tank, and the tank can only withstand a water pressure of 185 kiloPascals. Assume the density of water is exactly 1000 kg/m3, gravity is 9.8 metres/s2, and disregard atmospheric pressure.

How many cubic metres of water can safely be stored in the tank? Round DOWN to the nearest whole number (since rounding up could be catastrophic in this instance!), and please submit only a number with no other information.

Yeah... i can't do this... lol

i got a 4 digit number with a sum of digits being 26.

NOT saying this is correct -- just throwing it out there to see if anyone can confirm.

Oh, really??? i was at one, then i added 3, then counted 5 more, then counted 7 more, then counted 9 more, then counted 11 more... I just kept adding 2 more and counting it... -__-"

4 digits, but sum of 13.

Nope, found my mistake - 4 digits, sum of 26.

For those trying to solve it:
Pressure = height x density x acceleration due to gravity
Once we have the height of the water in the tank, look at spherical caps to find the volume that isn't occupied by water.

Okay, to elaborate the answer, now that the solution is out:

Pressure is force per unit area. However, pressure of a liquid on the bottom of its container can also be expressed as depth (height) of the liquid times the density of the liquid times the acceleration due to gravity.

Now the tank can handle a maximum of 185 kiloPascals or 185000 Pascals. The maximum pressure will occur at the bottom of the spherical tank, since that is where the water is deepest. So,

185000 Pascals / (1000 kg/m^3 * 9.8 m/s^2) = 18.877551 m as the height of the water. (Pressure divided by density times acceleration)

That means (since the radius of the tank is 12 meters, making the diameter 24m), that there will be 5.122449 meters at the top of the tank that is unfilled.

Now the volume of a sphere is V = (4/3)*pi*r^3 (r = radius). So the total volume of the tank is (4/3) * pi * (12)^3 = 7238.2295 m^3.

The top part of the tank that isn't filled is called a spherical cap. If you take the volume of the spherical cap and subtract it from the volume of the sphere, you get the volume of water in the tank.

A nice spherical cap calculator is at http://www.1728.com/sphere.htm. (You can also look up all the formulas at Wikipedia.) We know the sphere radius (12) and the cap height (5.122449). Plugging these in, we find that the volume is 848.45 m^3. Subtracting this from the sphere volume, we get 6389.78 and rounding down as specified, we get the answer of 6389.

For the Chocolate Ball, a magnificent new sweet was created. It was made by taking a 4-centimetre-diameter sphere of nougat and coating it with 1-centimetre-thick layer of marzipan. Then the whole thing is covered in a layer of caramel, which is then coated with a 2-centimetre-thick layer of dark chocolate.

Nougat has exactly 21.3 calories per cubic centimetre, and marzipan has 24.1 calories per cubic centimetre, and caramel has 18.7 calories per cubic centimetre, and dark chocolate has 16.2 calories per cubic centimetre. If the caramel makes up exactly 40% of the total calories of the sweet, how many total calories is this particular sweet? Please round to the nearest whole number, and submit only a number with no other information.

Prize is a Milk Chocolate JubJub Cake

For comparison purposes, I came up with 5 digits, sum of 21.

My method was to set it up in Excel and tweak the thickness of the caramel layer until it came out to 40% of the total. You can solve it using algebra to determine the thickness of the caramel layer, but I was feeling lazy.

solving the equation using algebra seems a huge waste of time - it's a a complex cubic equation.
so lennyfan's method is most recommended!

same, 5 digits, digit sum 21

i did the long algebraic way haha. had no choice, was on ipod for internet!

i came up with 4 digits, sum of 11... >__< i have to check the thickness of the caramel, don't I/ i just skipped that... >__<

yeah the caramel thickness is a bit key to the puzzle...

Ahhhh... I'm nopt gonna solve it. i could, if i wanted, but i don't... It would take so LONg, and a little candy with calories in the 10 thousands? Wuuuuut?

EDIT: Well, maybe it isn't so little... -__-"

Skipping this one cuz you can tell like a bunch of ppl will answer right

*lol*