Lenny Conundrum #167

stampsyne · **Posted:** Wed May 17, 2006 10:04 pm

Quote:

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 166). You have won 324 NP! Because you were in the first 250 to guess correctly, you also have been awarded a Yellow Buzzer Plushie, and receive a trophy and the Lenny Conundrum avatar!

Geraptiku :

Officer 1BDI · **Posts:** 1873 **Joined:** Sun Jan 01, 2006 9:50 am

Just submitted my answer. I don't think it's right, but you can't really take your time with an LC.

Edit: Oh, right, the question:

Quote:

Fifteen different farmers each had their own apple orchards. The first farmer had only one apple tree in his orchard, the second farmer had two trees in his orchard, and so on up to fifteen trees for the fifteenth farmer.

At harvest time, each farmer noticed something very peculiar: each tree in the same orchard produced the exact same number of apples. (Note that the number of apples per tree varied from orchard to orchard) And when all fifteen farmers got together to talk about it, they all realized that, if the farmer with eleven trees had given one apple to the farmer with seven trees, and the farmer with fourteen trees had given three apples each to the farmer with nine trees and the farmer with thirteen trees, they'd all end up with the exact same number of apples!

How many apples did all the farmers produce, in total?

AySz88 · **Posted:** Thu May 18, 2006 3:28 am

Oh dear, there are multiple solutions - though only one of the solutions makes any sense, so I'm going with that one. (i.e. I doubt a tree can produce more than 300,000 apples...)

BrunosisShale · **Posted:** Thu May 18, 2006 4:29 am

Math equation-wise, I think I may be able to do this one. -cranks out notepaper, calculator, and pencil- I highly doubt I'll get a trophy, though. Unless of course, everyone submits the wrong variant . . . D:

endeavourl · **Posts:** 1247 **Joined:** Thu Sep 29, 2005 9:34 pm

Go with the simplest solution.

The answer that I got is a number that has factors of 2, 3, and 5

sirclucky · **Posted:** Thu May 18, 2006 1:30 pm

I am so entering my approx 5.5 million solution. Or maybe the 10. somthing million solution. Seriously, this thing repeats around 360 thousand apples per tree. Meaning there are indeed an infinite number of solutions.

edit: Don't bother with the messy math on this one. Just use an excle spread sheet, find the right formula to use, and crank out an answer(or three answers, if you did it the way I did)

poohroony · **Posted:** Thu May 18, 2006 1:38 pm

sirclucky wrote:

I am so entering my approx 5.5 million solution. Or maybe the 10. somthing million solution. Seriously, this thing repeats around 360 thousand apples per tree. Meaning there are indeed an infinite number of solutions.

edit: Don't bother with the messy math on this one. Just use an excle spread sheet, find the right formula to use, and crank out an answer(or three answers, if you did it the way I did)

I used excel too but I just listed down all their multiples and found their greatest common factor

and I didn't get millions, just a few thousand apples

forcesinbalance · **Posts:** 101 **Joined:** Mon Nov 21, 2005 1:41 pm

Since this puzzle involves trees, I decided it would be appropriate to formulate equations for the apple-swappers and find their roots.

Then I picked the first set of roots that didn't result in any trees giving fractional apples.

kc_6201 · **Posted:** Thu May 18, 2006 6:33 pm

I JUST submitted my answer so no item for me. I didn't use a graphing calculator just good old trial and error.

matchbow · **Posted:** Thu May 18, 2006 8:09 pm

I'm trying it out in excel, but i don't know how it can just tell you an answer. i have to keep changing the base to check an answer. and since the answer is millions, this will take forever.

kc_6201 · **Posted:** Thu May 18, 2006 11:28 pm

My answer isn't in the millions. It isn't even close.

sirclucky · **Posted:** Fri May 19, 2006 2:30 am

There is an answer that isn't millions, but there is also an infinite number of answers, and only one of them is under 5 million.

As a hint, if you are doing it in excel, remember that every tree needs to spout a whole number of apples. Thus the 15 plot tree needs to each spout a whole number of apples. Instead of looking at "What if there was a total of one apple... two apples... three apples" try looking at "What if each of the 15 apple trees spouted 1 apple? 2 apples? ..."

AySz88 · **Posted:** Fri May 19, 2006 4:53 am

My hint: Modular arithmetic (http://www.cut-the-knot.org/blue/Modulo.shtml).

Officer 1BDI · **Posts:** 1873 **Joined:** Sun Jan 01, 2006 9:50 am

Quote:

Dear -----, Congratulations! You have guessed correctly in the Lenny Conundrum game (round 167). You have won 386 NP! Yours Sincerely, The Neopets Team! Web : http://www.neopets.com Dont forget to tell your friends about us - send them a greeting at http://www.neopets.com/sendgreeting.phtml.

...I'm shocked. I honestly thought I botched that answer. I'm a bit disappointed that I didn't get a trophy, because I started on it almost the minute it came out.

And I can't even remember what I put down! :cry:

I remember it was relatively small, though, like 2100 or a similar figure.

kc_6201 · **Posted:** Thu May 25, 2006 2:26 am

The answer was 1800. 120 apples per orchard.

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Lenny Conundrum #167

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