NeoPets Riddles (Lenny Conundrums) and Answers Here

did u make that chart for us to use or did u find it somewhere?

great job spazztic!

Another way to look at this is that each 2x2 bock of letters with a "dot" in the middle needs to be rotated one place counterclockwise. In which case, the chart should be:

2,10,4,12,6,14,8,16
1,9,3,11,5,13,7,15
18,26,20,28,22,30,24,32
17,25,19,27,21,29,23,31
34,42,36,44,38,46,40,48
33,41,35,43,37,45,39,47

That's how I did it also.

[So, what was the correct answer to the Bilge Dice problem?]

it was 1555....but some people complain cuz TNT ask for odds or whatever and they put 1554 and TNT didn't accept their answer

Do we have a board for clues on the mystery pic anywhere?

I don't understand the riddle for Lenny Con.!!! Any clues?

Are you referring to the latest riddle -- which was answered last week -- or to some earlier riddle?

Eliz.

new lenny
A large birthday cake was baked to celebrate the 6th birthday of Neopets. It was a round cake, made of two layers of vanilla cake; each layer was 18 inches in diameter and 3.5 inches tall. Between the two layers was a quarter inch of chocolate frosting. And covering the top and side of the cake was 3/8" of buttercream frosting.

If the vanilla cake has 140 calories per cubic inch, and the chocolate frosting has 320 calories per cubic inch, and the buttercream frosting has 470 calories per cubic inch, how many 800-calorie servings are in the cake? Please round down to the nearest serving.

Volume of right circular cylinder with radius "r" and height "h" is given by "V = (pi)(r^2)(h)". For one layer of cake, r = 9 and h = 3.5. Then the volume VL of one layer is:

. . . . .VL = (pi)(81 sq. in.)(3.5 in.) = 283.5(pi) cubic inches

Volume of two layers:

. . . . .2VL = 567(pi) cubic inches

Then the cake-calories are:

. . . . .(140 cal/cu. in.)(567(pi) cu. in.) = 79380(pi) calories

The frosting between the layers forms another cylinder, this time with r = 9 but h = 0.5. The volume VC of chocolate frosting is then:

. . . . .VC = (pi)(81 sq. in.)(0.5 in.) = 40.5(pi) cubic inches

The chocolate-frosting-calories are:

. . . . .(320 cal/cu. in.)(40.5(pi) cu. in.) = 12960(pi) calories

The buttercream frosting across the top may be regarded as another cylinder. But we need to remember to add the extra 0.375 inches to the radius, to account for what is on the sides. So this time, r = 9.375 and h = 0.375, so the volume VBT of buttercream on the top is:

. . . . .VBT = (pi)(87.890625 sq. in.)(0.375 in.) = 32.95898438(pi) cubic inches

The buttercream frosting around the sides may be regarded as a hollowed-out cylinder with outer radius 9.375 and inner radius 9. The height is the sum of the heights of the two cake layers and the chocolate frosting between them: 3.5 + 0.5 + 3.5 = 7.5. The volume VBS of the buttercream frosting on the sides can be found by finding the volume of the entire cake-and-frosting cylinder, and then subtracting out the cake:

. . . . .VBS = (pi)(9.375^2 sq. in.)(7.5 in.) - (pi)(81 sq. in.)(7.5 in.) = 51.6796875(pi) cubic inches

The total volume VB of buttercream frosting is the sum of these two volumes:

. . . . .VB = VBT + VBS = 84.63867188(pi) cubic inches

Then the calories from buttercream frosting amount to:

. . . . .(470 cal/cu. in.)(84.63867188(pi) cu. in.) = 39780.17578(pi) calories

The total calories for the cake are:

. . . . .79380(pi) cal + 12960(pi) cal + 39780.17578(pi) cal = 132120.1758(pi) calories
. . . . . . . = 415067.7736 calories (approximately)

Dividing by 800 calories per serving, we get:

. . . . .415067.7736 ÷ 800 = 518.834717

...or, rounding down, 518 servings.

It's late; I'm tired: Check my work!!

Eliz.

I made it. Sorry about the delay in response, I generally check out the forums only when a new conundrum is listed...

143
A large birthday cake was baked to celebrate the 6th birthday of Neopets. It was a round cake, made of two layers of vanilla cake; each layer was 18 inches in diameter and 3.5 inches tall. Between the two layers was a quarter inch of chocolate frosting. And covering the top and side of the cake was 3/8" of buttercream frosting.

If the vanilla cake has 140 calories per cubic inch, and the chocolate frosting has 320 calories per cubic inch, and the buttercream frosting has 470 calories per cubic inch, how many 800-calorie servings are in the cake? Please round down to the nearest serving.

I assume you're posting a correction, but I'm afraid I don't see how this version differs from the earlier version of the puzzle posted about three hours ago.

Please specify: what am I missing?

Thank you.

Eliz.

Elizabeth - looks good to me, but I'm tired, too LOL good work!

Lyk

workings?
hey stapel,
you seem to have done a good job apart from one thing...
"Between the two layers was a quarter inch of chocolate frosting"



why 0.5?

I take it the cake goes buttercream, vanilla, choc, vanilla hence there is chocolate frosting between the two vanilla layers - only one layer at 0.25in.

if i change that cell in my excel sheet from .25 to .5 i get the same answer as you so i think the rest of the working was ok.

but then again. maybe i'm misinterpreting the question and you have it right!
Ryan

It says a quarter of inch by the chocolate layer indeed

But the rest of the work is the same as mine

The only thing I'm not sure about is that the 3/8" buttercream layer could be seen as a layer on both sides of the cake. So that r would be 9.75. But since nobody seems to see it that way, it's probably just me reading the wrong thing

"Radius" is not the same as "diameter". The radius counts only from the center to the outside. As such, one would add only the 0.375 inches on the one side of the cake when considering the buttercream frosting.

But yes, the "h = 0.5" for the chocolate frosting between the layers should be "h = 0.25". So....

. . . . .VC = (pi)(81 sq. in.)(0.25 in.) = 20.25(pi) cubic inches

Then the calorie count for this bit is:

. . . . .(320 cal/cu. in.)(20.25(pi) cu. in.) = 6480(pi) calories

The adjusted calorie total for the cake then is:

. . . . .79380(pi) cal + 6480(pi) cal + 39780.17578(pi) cal
. . . . . . . .= 125670.1758(pi) calories
. . . . . . . .= 394710.2532 calories (approximately)

Dividing by 800 calories per serving, we get:

. . . . .394710.2532 ÷ 800 = 493.3878165 (approximately)

...or, rounding down, 493 servings.

Hope that helps a bit.

Eliz.

Nice Work
Thnx Eliz!!! I come here quite often for the lenny anwsers when I'm stuck, And this one made me stuck!!! You broke it down nicely, I pretty much understand it now. (I really have never been good at radius, area, that sort of thing..... )

Not sure why, but I'm off by 3 servings...

My calculation up to the frosting are same as yours... but the frosting ammount differs in my version:

1: frosting on top of the cake
pi * 9^2 * 0.375 * 470 = 14276.25 * pi

2: frosting around cake. Height this time is 3.5 + 3.5 + 0.25 + 0.375 = 7.625in, ourter radius is 9.375, inner radius is 9:

outer: pi*9.375^2 * 7.625 * 470 = 314978 *pi
inner: pi*9^2 * 7.625 * 470 = 290283.8 *pi

so total frosting callories are (314978-290283.8+14276.25) *pi=38970.53*pi= 122429.5

With two other figures being the same as in your calculation my total calorie count was 392166.7, which makes 490.21 servings or 490 complete servings...

so is it 490 or 493?