Lenny Conundrum

Every week, The Neopets Team releases a new Lenny Conundrum puzzle, and each week that puzzle gets posted on our blog. You can discuss with others the answer in the comments and come up with a solution! We also discuss the Mystery Picture Answers aswell!

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Wednesday, September 21, 2011

Lenny Conundrum - Round #421

Samrin has been having trouble with a very hungry Babaa eating all the grass and leaving none for the other Petpets. He decided to separate the Babaa from the others, but the only area Samrin had left in his field was a hexagonal patch, each side measuring 40 yards.

Samrin tied the Babaa to a post in one corner of the field using a 50 yard rope, and he knows it takes the Babaa 13 minutes to eat 1 square yard of grass.




How many days before the Babaa runs out of food and Samrin has to tie it to another post?
Round to the nearest whole day.

71 comments :

  1. I hope it's 27, that's also what I submitted.

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  2. Already got it..it's a three step math equation (three steps as in three shapes to define). You guys are off :/

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  3. (50^2*pi/3-2*10^2*pi/6)*13/60/24
    That's the formula I used. Am I right?

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  4. no that is not the right formula ya showoff !!!

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  5. You guys do understand that the rope is 50 yards...not 40. So there is a triangle, rectangle, and half of an ellipse. Calculate the areas of each, and then divide the right stuff.

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  6. ur formula doesnt even show how many days just a date9which from now would be in 13 years)

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  7. According to the formula, it's 23 days

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  8. the rope doesn't even come into play...just a distraction

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  9. The rope does come into play because the babaa is defined in area by how long the rope is.

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  10. The rope comes in to place if you use the formula for a triangle.

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  11. No, the rope is a huge part of the problem. It limits the Babaa to a circular area

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  12. No doubt I am wrong - but I got 22 days
    figured with 2 triangles and two rectangles.

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  13. I got 22.7 so I rounded to 23

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  14. Not very good at math are you guys? The rope acts like a radius of a circle. Don't know where all those polygons came from

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  15. The answer is by finding the area of a baseball field and dividing to find the right time. But there is no equation for the area of a baseball field. Good luck ;D

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  16. the baseball field is a square I believe. Finding the area would be easy, though I don't think that's the right answer.

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  17. baseball fields are a pentagon with one side being rounded ;D

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  18. It's 22.

    How many days **BEFORE** the Babaa runs out of food and Samrin has to tie it to another post?

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  19. OH GOD YOU'RE RIGHT.
    It is 22 if that's the case.
    Trick question.
    I did all the math and submitted 23.
    Damn.

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  20. I'm thinking it's 22 since that one person pointed out that it says BEFORE.

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  21. Ugh, if only TNT would word their questions properly. D: I frequently get one wrong because it isn't worded clearly.

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  22. Yeah, I bet it's actually 22 and a lot of us got it wrong because it seems to be 23. Or the other way around. Maybe the answer IS 23 but it really should be 22, since it has the word BEFORE. Only time will tell which one is right.

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  23. Or TNT clearly stating whether we're meant to take the nearest whole day before or the just nearest whole day. I mean, the 'before' could just be the way they say it, and we took it overboard. Or they could've meant that specifically.

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  24. So, those of us who answered in the first 30 minutes; do you think we made the top 250? I just want the avatar. :x

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  25. So final answer is...?

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  26. I did this:
    ((((50^2)pi/3)-((10^2)pi/3))*13)/(24*60)

    one third of a 50-yard radius circle minus one third of a 10-yard radius circle multiplied by 13 minutes, divided by 24 (hours) and 60 (minutes)

    sent 23

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  27. I just went on one account, send 22. Went on a different main account and went on 23.

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  28. The answer is 22.2955537838 which rounds to 22.

    The sector is not 1/3 of a circle.

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  29. Well. I submitted 22. Not like I need to worry about the trophy/avvie, since I'm way late. xD

    but ya. I think 22 is the right answer.
    Guess we'll know in a week (;

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  30. my answer is 23 (22,6892803)

    (pi*50^2/3-(pi*10^2/3))*13/60/24

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  31. You are all wrong. If you divide the hexagon in six triangles and find the area of each triangle and multiply the triangles by six. They are equilateral which makes it easy.

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  32. haha to anonymous! who says the babaa can reach all the grass? the rope is only 50m long! im in my second year of university mathematics degree and i submitted 22 and 23 on different account due to the "before" issue

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  33. Abanks:

    Why would you submit 23 when the rounded answer is only 22?

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  34. the shape forms an irregular pentagon (which is half of a hexagon) find area for hexagon and divide by 2... times by minutes per square foot and convert to days. you people and your overcomplicated equations

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  35. also the *before* will not make a difference. the babaa runs out of food at the end of the day, so technically the day it runs out of food will still count towards the amount of days passed.

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  36. P.S none of you have the correct answer so far. >:D

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  37. Abanks must be bottom of his class because im a high school grad and i can figure this out no problem.

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  38. uwhfibsdhzkjgh i forgot to include the curve :'( apologies to Abanks, although doing it the way i did for the pentagon part and solving the area of the circular part with pen and paper is a lot easier than what most of you guys were trying to do

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  39. the answer is 22. Comes out to 22.2955537838 (as markr said) rounded that comes to 22 days. The babaa runs out of food at the END of 22 days therefore the day it runs out of food counts towards the total amount of days since that day has already passed at the point which the babaa will run out of food. The wording isn't bad, you guys are just bad at word problems.

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  40. I'm just an eleven year old kid and so far i've got the complete area of the hexagon. It's 4030 square yards. I basically split the hexagon in half and worked out the area of the trapezium. (Not that anyone cares......)That's all! Dont know how to do the rest so i'm just going to put 22. Thanks!

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  41. Person who's picking her nose23 September 2011 at 04:17

    I was previously known as 'random' so it's still me. Can someone tell me how to do it? Continued from where i left off please? thx!

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  42. I got 21 days, 21.116 to be exact. I used integrals by confining the circle by y=-2.25x+72 and y=-2.25(x+72)+72, i.e. y=y=-2.25x-90.

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  43. ^Edit to above -- and the x-axis, of course.

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  44. Ok guys... 50 comments and not even a single solid explanation. I've read about squares, triangles, rectangles, trapeziums... but all is about circular sectors.

    http://imageshack.us/f/706/babaa.png/

    Hope it helps (:

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  45. Ilere -- I don't think that your calculation of the area of the triangles are correct. Do you mean that B=base? I don't see why you could give the formula of the area of a circle to find the base (the arc length). That's where you lost me.

    I still say that integration is the way to go. Put it on a cartesian plane, set the boundaries, and there you go.

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  46. Ilere smartpants

    The blue part isnt a circular sector, therefore you cant calculate the radius as 10

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  47. Anonymous --- B is the area of the blue circular sector, sorry ;) I didn't want it to be confused with the first area calculated.

    2nd Anonymous --- Fatal error I didn't noticed :(. At first I tried to calculate it as a triangle, but then I realised the curved line. Now I see it's not really a circular sector D: I don't know really how to calculate the area of the blue parts; but I think that the circular sectors/ triangles ones seem to be pretty accurate (it may change a few decimals).

    Once again, sorry. I just tried my best ;).

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  48. If you guys want, I'll tell you what I did in detail. This is using calculus.

    For the hexagon -- the only parts of the hexagon that affect the Baabaa are the bottom half and the top right diagonal.
    The equation for the bottom right diagonal is:
    y2 = 2.25x
    The equation for the top right diagonal is:
    y3 = -2.25x + 72
    The equation for the bottom left diagonal is:
    y 5= -2.25(x + 72) + 72
    The bottom line is the x-axis.

    The equation for the circle (which only provides the top half, which is all we need) is
    y 1= sqrrt(2500-x^2), or x^2 + y^2 = (50)^2
    This is the area in which the Baabaa can move.

    Now, if you follow the formulae correctly, you will see that the overall hexagon ranges from xmin = -56 ; xmax = 16 and ymin = 0 and ymax = 72.

    What I did from there is divide it into 4 triangles and a rectangle, which is what most of you did as well.This gives us one triangle that is completely filled by the circle, and two that are partially filled up by the circle's area (bottom left and top right triangles).
    The rectangle portion is from xmin = -40 ; xmax = 0 and ymin = 0 and ymax = 72.
    The bottom right rectangle is confined in xmin = 0 ; xmax = 16 and ymin = 0 ; ymax = 36.
    The top right rectangle is confined in xmin = 0 ; xmax = 16 and ymin = 36 ; ymax = 72.
    And, finally, the bottom left rectangle is confined in xmin = -56 ; xmax = -40 and ymin = 0 ; ymax = 16.

    Okay, now we can start finding the areas. The bottom right triangle is the easiest, as it's completely filled up by the circle. Looking above, we see that the base is 16 and the height is 36, so the area = (1/2)(36)(16) = 288.

    The next-easiest one to do is the rectangle. This is where we start integrating.
    So, we take the integral S, from x=-40 to x=0, of y1 [sqrrt(2500-x^2)]. This will give us 1759.12.

    Next we will do the bottom left triangle. Keep in mind that you DON'T integrate from x=-56 to x=-40, but rather from where the two intersect. If you combine the functions, you'll find the zero at x = -47.258.
    So, we integrate S, from x=.47.258 to x=.40, of y5 [-2.25(x + 72) + 72]. We get 115.093 for the area.

    The last one to integrate is the top right triangle. We're going to actually split this triangle into two more pieces. One will stop where y1 and y3 combine, as we did with the last triangle. However, there's a little completely-filled triangle to the right of that area, so we have to count that as well.
    We find that the functions intersect at (10.2497, 48.9382). We can't simply take the zero for this one, because the y-value is important as well as the x-value.
    Ok, so we take the integral S, from x=0 to x=10.2497, of y3 - y1 - 36 [(-2.25x + 72) - (sqrrt(2500-x^2)) - 36]. The -36 at the end is so that we don't count the rectangular area below the top right triangle, which would be the bottom right triangles times 2.
    When we finish the integration, we get 139.884.
    For the little triangle, we take the coordinates (10.2497, 48.9382). We see that the base length is (16-10.2497) and that the height is (48.9382-36). So, the area is (1/2)(5.7503)(12.9382) = 37.1993.

    Now we add up all the areas we got, starting at the beginning.

    288 + 1759.12 + 115.093 + 139.884 + 37.1993 = 2339.3 square yards.

    One square yard = 13 minutes

    2339.3 yards * (13 minutes/1 yard) = 31,410.9 minutes.

    31,407 minutes * (1 hour/60 minutes) = 506.848 hours.

    506.783 hours * (1 day/24 hours) = 21.1187 days. The question says simply to round to the nearest whole day, so 21 should be the correct answer.

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  49. 2 equilateral triangles with 40 yd sides and two rectangles 40 x 10. 2,400 sq yds x13 min/yd = 31,200 min /60 = 520 hr /24 = 21.6 so 22 days.

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  50. I wouldn't be surprised if the answer was actually in the 40s... Supposing this Babaa actually needs to sleep sometimes and can't just eat constantly for a straight month.

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  51. Sorry, as a quick edit to my calculus explanation above:

    I said:

    288 + 1759.12 + 115.093 + 139.884 + 37.1993 = 2339.3 square yards.

    One square yard = 13 minutes

    2339.3 yards * (13 minutes/1 yard) = 31,410.9 minutes.

    31,407 minutes * (1 hour/60 minutes) = 506.848 hours.

    506.783 hours * (1 day/24 hours) = 21.1187 days. The question says simply to round to the nearest whole day, so 21 should be the correct answer.


    I jumbled up a few numbers in there. 2339.3 is correct, but
    2339.3 yards * (1 hour/60 minutes) = 30,410.9, not 31,410.9 minutes

    The calculation for hours is correct, but I wrote 31,407 instead of 30,410.9 again, and the answer of 21.1187 is still correct.

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  52. you noobs are so dumb rofl the angle is 120 degrees find the area of the sector and divide by 13mins, then by 60, then by 24 xD

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  53. Isn't this just a simple math problem? What is it with the use of calculus and getting a wrong answer in the end? Just use simple trigo to solve it. Answer is 22.29... Let the hexagon be ABCDEF, A is where the babaa is and you label the rest clockwise. Then extend AB and AF to 50 yards and draw the 120 deg sector of circle. Let the arc of the circle intersect BC and FE at G and H respectively. Ok that is your diagram, now the math.
    From trigo, AF/sin(angleAHF) = AH/sin(angleHFA)
    we know AF=40, AH=50, angleHFA=120 deg, one unknown angleAHF, easy to find, you get angle AHF=43.8537786..... Deg and you are almost done.
    AngleHAF=16.14622139...., deg triangle angle sums to 180
    It is easy to see that triangle AHF is congruent to triangle AGB.
    AngleGAH= 120-2*16.14622139=87.70755722..
    total area babaa covered= Area triangle AGB+ Area triangle AHF + Area sector AGH = 2*0.5*AH*AFsin16.14622139 + pi*50*50*87.70755722/360
    sine you know AH=50, AF=40, you can easily solve total area=2469.661342....
    then 2469.661342*13/(60*24)=22.29555. hence answer is 22.

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  54. i flunked calculus so my baabaa broke his rope and ate it all in 2 days:)

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  55. After a long hour of calculation using the sine rule and everything, I got 22.2956475.. days.

    And just when I was about to submit the answer, I realise the round ended already. This is the very first time I worked so hard to solve the question despite the fact that I have not touched math for 3 years :(

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  56. just got the message... the correct answer is 23

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  57. http://www.neopets.com/games/conundrum_feature.phtml?round=421

    23 days

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  58. I got a gold trophy!! ^^

    The answer was 23.

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  59. What... This doesn't make any sense, why is the answer 23? can get neopets to explain? They certainly didn't say round up...

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  60. But if you round down, it means the babaa runs out of food before the day is over. You HAVE to round up.

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  61. I had worked it out at http://wiki.pachogrande.com/math-puzzles/lenny-conundrum---round-421 at 22 days.

    Their answer doesn't match their instructions - if they wanted it rounded up to nearest whole day then it should say that. The question asks which day the goat runs out and needs to be moved - he needs to be moved on the 22nd day. If you move him on day 23 then he's been starving most of the day.

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