NeoPets Riddles (Lenny Conundrums) and Answers Here

ummm from where did you get a kite shape? Funny looking kite, it's more like a tangram

My answer was 930 (rounded up from 929.022)

921

outside edge is 3200/7
northwest diagonal is sqrt(200^2 + (1000/7)^2)
northeast diagonal is sqrt(200^2 + (600/7)^2)

oh 934. my first answer was closer T.T

Actually, I think it's worth going into that trig, because I'm not getting an equilateral triangle out of it.

In terms of the kite, I have:
D1 (long diag) = 200*(sqrt 2)
D2 (short diag) = 2*((400*400)/7) / D1
D2 = 1600 divided by 7*(sqrt 2)

D2 / 2 = 800 / (7*(sqrt 2)) = side A of the big right angle of the kite.
D1 - (D2/2) = side B of the big right angle of the kite.
B = 200*(sqrt 2) - 800/(7*sqrt 2)
B = 2800/(7*sqrt 2) - 800/(7*sqrt 2) = 2000/(7*sqrt 2)

A*A + B*B = C*C
((2000*2000)/(49*2)) + ((800*800)/(49*2)) = C*C
(4640000/98) = C*C, (2320000/49) = C*C
(200*(sqrt 58))/7 = C

Now along the top, we see that Angle X of the first field + Angle Y of the big right angle of the kite + Angle Z of the small right angle of the kite = 180 degrees. We already know that Angle Z = 45 degrees.

sin Angle Y = A/C
sin Angle Y = (2000/(7*sqrt 2)) / (200*(sqrt 58))/7)
sin Angle Y = 10/(sqrt (2*58))
sin Angle Y = 10 /2*(sqrt 29) = 5/(sqrt 29)
Angle Y = 68.19859

Angle X + 68.19859 + 45 = 180
Angle X = 66.80141

Some more trig eventually lets you work out that the last remaining side of the fence is approx 245.7807.

Add them all together:
245.7807
1600/7
800/7
800/7
(200*(sqrt 58))/7

245.78
228.57
228.57
217.59

Total = 920.51 - round up to 921

I got the same as maidm.

Actually, the answer is much more simple than that:

We know that each square side is 400 m, the total area of the square is 400² = 160,000 m².

Therefore, every Area section is 160,000 m²/7 = 22,857.14 m².

Look at he upper triangle (A triangle), we know the Area of a triangle is base x height / 2, and the height of the triangle is exactly the middle of a side:

A Area = Base A (200 m) / 2
22,857.14 m² = Base A (200 m)/2

Base A = 228.57 m (first fence section)

Divide "kite" section in 2 (B1 and B2). The whole square can be divided in 2 section, going from the bottom left corner to the upper right corner, this part contains sections C, D E and B2:

Area middle square = B2 + C + D + E
160,000/2 m² = B2 Area + 22,857.14 m² + 22,857.14 m² + 22,857.14 m²
B2 Area = 11,428.57 m²

The area of B2 can be expressed as:
B2 Area = z (200 m)/2
11,428.57 m² = z (200 m)/2

Z = 114.28 m (second fence section)

The area of B1 is B Area - B2 Area:

B1 Area = 22,857.14 m² - 11,428.57 m²
B1 Area = 11,428.57 m²

The area of B1 can be expressed as:
B1 Area = x (200 m)/2
11,428.57 m² = z (200 m)/2

X = 114.28 m (third fence section)

Y = 400 m - x - 228.57 m
Y = 400 m - 114.28 m - 228.57 m
Y = 57.15 m

The side "a" from the A1 triangle is 200 m - y = 200 m - 57.15 m = 142.85 m

With Pitagoras's theorem:

c² = a² + b²
c = square root ((142.85m )² + (200 m)²)
c = 245.77 m (fourth fence section)

e = 200 - z
e = 200 - 114.28 m
e = 85.72 m

With Pitagoras's theorem:

f² = d² + e²
f = square root ((200 m)² + (85.72 m)²)
f = 217.59 m (fifth fence section)

The total is :

228.57 + 114.28 + 114.28 + 245.77 + 217.59 = 920.85 m

round to 921 m.

Same answer, different method.

To everyone that shared I would like to say Thank You & Good Luck!

It's even simpler than that. Each triangle owns 1/7 of the perimeter of the square.

Base A = 1600/7
x+z = 1600/7
due to symmetry, x = z

z = 800/7
e = 200 - z = 200 - 800/7 = 600/7
f = sqrt(200^2 + e^2)

y = 400 - (Base A + x) = 400 - (1600/7 + 800/7) = 400/7
a = 200 - y = 200 - 400/7 = 1000/7
c = sqrt(200^2 + a^2)

solution = Base A + x + z + c + f

Excellent observation, but remember, in math you need to demonstrate, not assume.

Lenny Con-whats a face
Hey! You guys are really good at maths! I already entered my GUESS for that one which was 291...lol...so I cant post the real answer! I only got how to figure it out after I read through EVERYTHING..although I didnt even understand more than half the symbols

Murci:

Which statement would you like me to demonstrate?

Each triangle owns 1/7 of the perimeter of the square.
or
x = z

...
Basically..im 11 years old and im not that good and im new to the lenny thing...i need neopoints after getting to lab map (woot!) and i owe my best friend some neopoints..so...i need 30k!

...
I actually think this is a good forum...i like it alot! omg..alot of stuff has happened when i took my hiatus...i better go out and collect some new avvies! btw..my neopets username is: sa_is_me
neomail me!

You are right, every section (not all are triangles) owns 1/7 of the perimeter of the square.

However, take a look at the upper left corner, that section (where I named "y") the horizontal side of the section is not equal to vertical one.

My point is, you need an stronger argument to say that x = z.

Re: ...


¿do yo need np? go here, and click in hard to find games, you can make 30k np very quick and very easy.

Yeah, I goofed calling them all triangles. However, I did state that x=z due to symmetry. It's fairly straightforward. Draw the diagonal from the lower left corner to the upper right corner. The two halves of the square are symmetrical because of the way it was partitioned. There are three pairs of equivalent sections plus the kite.

you are soooooooooooo right !! thanks for explaining it better.

The mistery pic is space faire doll in the how to draw section.

yer..but i dont really need guides. i just do it myself...thanks anyway ^^

Lenny Conundrum
http://www.neopets.com/games/conundrum.phtml

look at the website and can anyone help me with the answer?

Gilbert the Gelert farmer (He's a Gelert who happens to be a farmer, not a farmer who grows Gelerts!) grows crops on a square field, 400 metres on a side. He has divided this field into seven different sections, such that each section has the same area, and each section meets at a point in the exact center of the field.