NeoPets Riddles (Lenny Conundrums) and Answers Here

40% in decimal is 0.4
I haven't a calculator so power and i haven't excel

Not many know about this board. I had the correct answer from last week. It was also posted on this board yet only a few got it correct.

Nah, cuz we both have the avatar but we got smaller trophies.

revise that last post - I think you get a trophy for the first 250 but not sure where the cutoffs are.

Well, if you believe in cheating, go ahead.

I haven't trophy or avatar.....

First 25 get gold, next 75 get silver the remaining people until 250 get bronze. All 250 get the avatar and the prize given out.

Yup yup, that's right. =D

Judesalb I think that's because the correct answer was posted late on this board and on the neoboards, and a lot of people had already submitted the incorrect answer...

I guess we have different opinions on sharing.

i dunno if it enters into the equation... but... do leap years enter into this? so... add 4 extra days to it? so it will be 7304 days?

this is my first post to this board but i have been lurking for the last couple of conundrums trying to inspire me to get ideas... failed the last 2 though

TOO EASY
The sum of an infinite series decreasing by the same ratio can be calculated as (First Term)/(1-rate of decay).

Rate of decay is .4 (40%)

31416/.6=52360

I am absolutely certain this is correct.

In order to get a gold trophy you have to be in the first 10 people to submit the correct answer..
11-50 is a silver and the rest is bronze

I don't know if the answer I submitted was correct, but this was my thought process:

Since the "rate of decay" (As someone else calls it) is constant, I just typed in a simple formula (use the first two days to guide) into Excel and clicked-and-dragged.

I got sidetracked in the beginning thinking about leap years too, but ultimately decided that the impact of the extra days is negligible.

Until next week!

this is a little late since the new one is out but:

Dear kimmmmm,

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 214). You have won 2156 NP!

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

Yours Sincerely,
The Neopets Team!

yay =)

Dear Alice Suttle,

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 214). You have won 2156 NP!

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

Yours Sincerely,
The Neopets Team!

Silver trophy, wahey!

----

In regards to the current Lenny Conundrum, I highly doubt I'll be getting the right answer seeing as I'm AWFUL at maths, ha! Good luck to everyone else though!

i got the same as quogara

day one = 31614
day two = 31614 x .4
day three = 31614 x (.4)^2
.
.
.
sum (31614 x (.4)^n, n, 0, 365 x 20) = 52360

yes. I also got 52360

lenny
I would like to thank kenshin for the assistance last week. I was in the top 250 also. I knew that invisible was not right, but I didn't quite have it. I went the the grundo plushie, but didn't make the right connection.
As far as today's goes I post 52360 way over an hour ago, because it was the only thing I could come up with on my own. I didn't know if it was right I actually figured up the forty percent for about 22 days and the answers by then were .000 ... etc. with a whole bunch of numbers after it. Then I added up all those 22 numbers and rounded them. So I came up with what everyone here is coming up with now, but I was just not positive. Good luck to all of us.

lenny
Ya'll do all that complicated math that's over my head. I do mine the way I understand it. I'm glad we're coming up with the same answers.

People are already posting this to tutoring forums, pretending this is math homework ("and my whole grade, for the whole year, depends on it, so you HAVE to give me the answer NOW!!!"), so let's just hand out the answer here. I know many (most?) couldn't care less about the "how", but I'll include it anyway....

Assuming that partial fish are counted in the total, we have a geometric series, with r = 0.4. The first term is a = a_1 = 31416, with each new term being the previous term multiplied by r = 0.4.

The general term (the n-th term), a_n, is then a r^(n-1), so:

. . . . .a = a_1 = 31416
. . . . .a_2 = a r^1 = (31416)(0.4)
. . . . .a_3 = a r^2 = (31416)(0.4)(0.4)

...and so forth.

For a geometric series with first term "a" and common ratio "r", the sum of the first "n" terms is given by:

. . . . .S_n = [ a (1 - r^n) ] / [ 1 - r ]

In this case, we have a = 31416 and r = 0.4. We need only find the number of days in twenty years. Assuming a Neopian year is the same as an Earth year, we get:

. . . . .(356.25 days /year)(20 years) = 7305 days

The final terms of the series will be vanishingly small; for instance, a_366 (the first day of the second year) will equal zero, followed by a decimal point, followed by 140 more zeroes, followed by 177.... But those vanishingly-small terms do add up, so....

. . . . .S_7305 = [ 31416 (1 - 0.4^7305) ] / [ 1 - 0.4]

. . . . . . . . . .. .= [ 31416 (1 - 0.4^7305) ] / [ 0.6 ]

. . . . . . . . . .. .= 52360 (1 - 0.4^7305)

Unfortunately, this is more than my calculators (or Excel) can handle exactly; the parenthetical portion is evaluating to "1". Do with that what you will, but I would expect that the "correct" answer will be just "52360".

Eliz.