NeoPets Riddles (Lenny Conundrums) and Answers Here

And shame on you for saying it was deliberately posting wrong answers. You all had the same chance to point out the honest errors that I made... as you said, "I thought was a place to help popple out" Evil or Very Mad

and yet it was me that kept finding my own mistakes!

Incidently, for those looking for an alternate formula to calculate a Triangle's side from it's area:

=SQRT(4 * B2/SQRT(3))

works just as well as

=SQRT(2*B2/SIN(RADIANS(60)))

(And don't worry, I submitted my first answer without finding all those other mistakes as well.)

If you want the correct answer, plug one of these formulas into C2, and use the other formulas posted in the topic above describing the spreadsheet.

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For those willing to do their OWN work, instead of looking for the end answer:

Column A (titles): Square, Triangle, Circle, (totals)

Column B (areas): 183753.5, =B1/1.75, =B1/1.5, =Sum(B1:B3)

Column C (side length): =SQRT(B1), =SQRT(4 * B2/SQRT(3)), =2*PI()*SQRT(B3/PI())

Column D (Fence length): =4*C1, = 3*C2, =2*PI()*C3, =SUM(C1:C3)

Then plug numbers into B1 until D4 = 4000. The answer will appear in B1. (Don't forget to round)

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The starting value in B1 is incorrect.. it's simply a placeholder - which you then fiddle with to come up with an answer.

And if anyone finds a mistake in the formulas, by all means, post it.

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ok marty i believe in you my answer is in your hands

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marty formula
marty was plugging in numbers per formula would column d for the sum be sum of d1:d3 instead of c1:c3. after plugging in the numbers for the place holder b1 i came up with 831100. thank you for the formula. not sure if i am right just checking.

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You are correct sir! Good catch.

Sum for column D should be SUM(D1:D3)

I also saw posted on the NeoBoards:

Quote:

Best case: 1 big circle, with C=4000
Area of circle = 1,273,239

Worst case: 3 triangles, with side=4000/9
Area of 3xtriangles = 256,600

So answer must lie in there somewhere.

Which makes sense to me... answer MUST be 6 or 7 digits.

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a - side of the square
b - side of the triangle
r - radius of the circle
a,b,r > 0
a^2=1.5 * pi * r^2 - given -> r=a/sqrt(1.5 * pi)
a^2= 1.75 * sqrt(3)/4 * b^2 - given ->b = a/sqrt(1.75 * sqrt(3)/4)
4a+3b + 2pi r = 4000 - given -> 4a+3a/sqrt(1.75 * sqrt(3)/4) + 2pi a/sqrt(1.5 * pi) =4000 =>
a= 4000/[4+3/sqrt(1.75 * sqrt(3)/4) + 2pi/sqrt(1.5 * pi)] = 386.8211671
a^2 = 149630.6154
a^2+a^2/1.75 + a^2/1.5 = 334887.5677

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Same answer with the spreadsheet.

(I got 334887.5678, but what's a 10,000th of a point, when you're rounding to an integer?)

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FINALLY!
Congratulations! You have guessed correctly in the Lenny Conundrum game (round 177). You have won 602 NP!

Because you were in the first 250 to guess correctly, you also have been awarded a Magic Hat, and receive a trophy and the Lenny Conundrum avatar!

Yours Sincerely,
The Neopets Team!

***goes off to look at new conundrum before checking formulæ here*** :-P

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Disappointment...
Why wouldn't Neopets accept an answer for LC 177 in the same form in which the question was asked? Mad

"TEN" => "SQF"

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I got 334888 too...man, I love my graphing calculator!

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do u think that if I missed the answer by 1 nunmber they're not going to give me the price? I putted 334887 instead of 334888 :S

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I'm not a Neopetter, but why would they reward a wrong answer?

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but it's just 1 number! Razz

It was because I didn't round it up right...

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and they said directly to remember to round to whole number so nope they wont give it to ya.

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kristen1993 wrote:

hi marty, eliz, bizarre, purplemonkey, and all the rest of the regular gang and newbies also .... Bet I stumped ya's with a different user name. well that because I am having some trouble with mine, and well quite honestly... I dont care at the moment.
I am disappointed with how someone acted here with deliberately posting wrong information to mislead others. This I thought was a place to help popple out.... not deliberately give misleading information so they submit the wrong answer... this isn't the first time this has happened either.... I am just glad that I only come here to help others, 99% of the time, because my stepdad is a math professor at the university...so when I do get stumped he helps me out. I have not missed a mystery pic or a lenny for the past 2 years since I started playing.... sad that others cant help everyone else who may need help instead of having a burr up their butt.... If this message get posted.... anyone who looks at this board, please dent judge the rest of us by the way one or two people act. And please remember this is only a game on neopets.... you lost nothing if you submitted the wrong answer. Hopefully later today I can log in with my original account and if not, as long as I didn't get banned, I will be back in later. Have fun everyone Now....Mzthing is stepping down from her soap box!

I sincerely hope you do NOT think I deliberately posted an incorrect answer.
My post was a genuine attempt at solving this LC and if I got it wrong then I'm sorry for trying my best.
I post with good intentions of:-
1. Hoping I've worked it out and contributing to this board
2.Trying to show my reasoning
3. If what I post is wrong, or based on incorrect assumptions, wrong formula(s) or whatever, then I fully expect for someone more skilled to show me my errors in a constructive way, not just say it's wrong and dismiss me out of hand.
4. If I'm on the right track, then I hope it helps someone else.

If I was way off the mark, I apologise.

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Milarepa wrote:

Why wouldn't Neopets accept an answer for LC 177 in the same form in which the question was asked?
"TEN" => "SQF"

They did in a couple of them. I guess they didn't think to accept the encoded answer this time, which is slightly unfair. Then again, they seem to expect more people to put the answer straightforward, these days.

ethanxxx wrote:

do u think that if I missed the answer by 1 nunmber they're not going to give me the price? I putted 334887 instead of 334888 :S

They don't grade each answer [or they'd make you show your work, which would be a pain]. They accept only a few variants of the answer, like "10" or "ten" or "ten stars," but not "There are ten stars on the Magic Shop" because trying to think of every possible variation of the answer that people might submit would take forever.

In this case, being off by one counts as being wrong.

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:wink:

:wink:

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Jen Aside wrote:

Milarepa wrote:
Why wouldn't Neopets accept an answer for LC 177 in the same form in which the question was asked?
"TEN" => "SQF"

They did in a couple of them. I guess they didn't think to accept the encoded answer this time, which is slightly unfair. Then again, they seem to expect more people to put the answer straightforward, these days.

ethanxxx wrote:
do u think that if I missed the answer by 1 nunmber they're not going to give me the price? I putted 334887 instead of 334888 :S

They don't grade each answer [or they'd make you show your work, which would be a pain]. They accept only a few variants of the answer, like "10" or "ten" or "ten stars," but not "There are ten stars on the Magic Shop" because trying to think of every possible variation of the answer that people might submit would take forever.

In this case, being off by one counts as being wrong.

yo

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owlette wrote:

I sincerely hope you do NOT think I deliberately posted an incorrect answer. My post was a genuine attempt at solving this LC.... If I was way off the mark, I apologise.

Some people seem to feel that anybody who is willing to put in the effort to calculate the answers somehow owes them the prize-winning answer. They're wrong; you owe them nothing. You put in the effort, showed all your work, and were willing to accept correction. In my opinion, you have nothing to apologize for.

The 'Lenny' authors, in Round 178 wrote:

Gilbert the Gelert farmer (He's a Gelert who happens to be a farmer, not a farmer who grows Gelerts!) has three fields. One field is an equilateral triangle, one field is a circle, and one field is a square. The square field is 75% larger in area than the triangular field, and 50% larger in area than the circular field. In order to completely fence all three of the fields, exactly 4000 metres of fencing is required.

What is the total area of all three fields, in square metres?

Let "A_s" be the area of the square, "A_t" be the area of the triangle, and "A_c" be the area of the circle. Then:

. . . . .Since A_s = 1.75(A_t) = (7/4)A_t,
. . . . .then A_t = (4/7)A_s

. . . . .Since A_s = 1.5(A_c) = (3/2)A_c,
. . . . .then A_c = (2/3)A_s

Let "s" be the length of a side of the square field. Then A_s = s^2, so:

. . . . .A_t = (4/7) s^2
. . . . .A_c = (2/3) s^2

The perimeter P_s of the square is 4s.

The triangle is equilateral. Let "t" be the length of a side of the triangle. Then, by what is known of 30-60-90 triangles (one of which would form half of an equilateral triangle), we know that the height of the triangle is (sqrt[3]/2)t, so the area of the triangle is:

. . . . .A_t = (1/2)(t)((sqrt[3]/2) t)
. . . . .= (sqrt[3]/4) t^2

From our previous area equality, we then get:

. . . . .(sqrt[3]/4)t^2 = (4/7) s^2
. . . . .t^2 = (16/(7sqrt[3])) s^2
. . . . .t = (4s) / sqrt[7sqrt[3]]

Then the perimeter P_t of the triangle is (12s)/sqrt[7sqrt[3]]

Let "r" be the length of the radius of the circle. The area A_c of the circle is given by:

. . . . .A_c = (pi) r^2

From our previous area equality, we then get:

. . . . .(pi) r^2 = (2/3) s^2
. . . . .r^2 = (2/(3pi)) s^2
. . . . .r = (sqrt[2]s) / sqrt[3pi]

Then the perimeter (circumference) P_c of the circle is 2(pi)((sqrt[2]s) / sqrt[3pi]) = sqrt[8pi/3]s.

We are given that the total amount of fencing (thus, the total perimeter, assuming no overlap and no waste) is 4000. Then:

. . . . .4000 = P_s + P_t + P_c
. . . . .= 4s + (12s)/sqrt[7sqrt[3]] + sqrt[8pi/3]s
. . . . .= (4 + 12/sqrt[7sqrt[3]] + sqrt[8pi/3])s

Solving, we get:

. . . . .s = 4000/(4 + 12/sqrt[7sqrt[3]] + sqrt[8pi/3])

We don't need to evaluate this until the very end. Returning now to the area considerations, we get:

. . . . .A_s + A_t + A_c
. . . . .= s^2 + (4/7) s^2 + (2/3) s^2
. . . . .= (1 + 4/7 + 2/3) s^2
. . . . .= (47/21) s^2

Doing all the computations continuously in a calculator, we then get a total area of 334887.567696... square meters. Rounded to the nearest whole number, the answer would be "334888".

Please check my work. Thank you.

Eliz.

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