NeoPets Riddles (Lenny Conundrums) and Answers Here

nevermind, I figured it out. I got 4 digits with a sum of 9 as well.

so wait what is the answer

THIS WEEKS PUZZLE - ends Next Wednesday, most likely

First, find the greatest integer that can divide each of the numbers 283, 427 and 715 to leave the same remainder in each case. Then, take that number, multiply it by four, and subtract 11. That number is X.

If you take the number you get by placing the digit 7 to the right of number Y, it is equal to Y + X.

What do you get when you multiply X by Y?

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this was a fun one. my answer had digits with a sum of 11.

Agreed, sum of 11. And to be a bit more specific, 5 digits.

also, agreed

Last week's solution:

The ball is shot at an angle of 45 degrees to the ground with a velocity of 300 m/s. We should be able to split that initial velocity into horizontal and vertical components by dividing the the 300 by the square root of 2, since we have a 45 degree triangle to work with. The horizontal velocity should stay constant until it hits something, assuming no air resistance.

So at t seconds, the horizontal distance is d = 150*sqrt(2)*t.

The vertical velocity will be decreasing at the rate of 9.8 m/s. So the velocity at time t will be 150*sqrt(2) - 9.8*t. Integrating this to get the height, we get h = 150 * sqrt(2) * t - (1/2) * 9.8 * t^2 = 150 * sqrt(2) * t - 4.9 * t^2.

Now Terror Mountain rises at a rate of 30 degrees, so we are looking at a 30-60-90 triangle with a ratio of the sides of 1 : sqrt(3) : 2. This means the height at any distance into the mountain is (1 / sqrt(3)) times the distance into the mountain. So when the cannonball hits the side of the mountain, h = (1/sqrt(3)) * d.

This gives us 150 * sqrt(2) * t - 4.9 * t^2 = (1/sqrt(3)) * (150 * sqrt(2) * t)

A trivial solution is t=0, but that is when the cannonball is shot out, so we ignore that one. Dividing both sides of the equation by t and rearranging, we get: 4.9 * t = (1 - 1/sqrt(3)) * 150 * sqrt(2) , or t = 18.29746 s. Plugging this back into h = 150 * sqrt(2) * t - 4.9 * t^2 gives h = 2240.97 m. Rounding to the nearest metre gives 2241 m.

For future reference, the prize for this week is the book Cave Kacheek.

what does this mean
"If you take the number you get by placing the digit 7 to the right of number Y, it is equal to Y + X."

how do you mathematically set it up supposing the answer u get is "a"

There is no way as far as i know to set it up algebraically... I set it up exactly how it would look when you added it going down.... For example lets say you got x=100 (not the right answer), now set it up so it looks like this:

100
+
___
7 (visually line the 7 up on the right, my computer didn't line it up the same way i did, sorry) Obviously the last digit of y would be a 7 as 0 +7 = 7 . So now pencil in the 7 and then put another 7 in front of first 7, and just keep going like that... I didn't really understand that part of the question myself, took me awhile... and it took me awhile to come up with x, maybe it could have been done by a spreadsheet or something faster, but i solved it trying every combination possible starting at 283 down... I know I'm not in 250, but I'm happy to get it at all, been awhile since I knew I was right... I also got the 5 digits =11 answer... good luck:)

If you put the 7 to the right of number Y, what you are effectively doing is getting 10*Y + 7. Putting a new digit on the right moves all the other digits over 1 place, which is the same as multiplying by 10.

So it means 10*Y + 7 = Y + X.

Thank you Lennyfan. I couldn't understand what that sentence meant either until you explained it. Must be too tired to think straight

Thanks!!

Are you guys sure your right, my digits came out to a sum of 15.

Dear Emily,

Congratulations! You have guessed correctly in the Lenny Conundrum game (round 387). You have won 735 NP!

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

Yours Sincerely,
The Neopets Team!

And I did all the work myself -- didn't even look at this site till after to confirm!!! I knew I was right, didn't think I'd be top 250, took me awhile!!! YAYYYY, never would have thought it would be a math question i won too lol

the new puzzle is out: it's a graphic with a bunch of nonsense letters arranged in the shape of a circle. -- not sure yet it the circle is important.

and the prize is Jhudora-themed.

Here are the letters:
GBWHGYW
OBUSKIRTXXEDYF
EOIUFKHYMGTJNCHR
VTSHOTAQZNCWNCBZ
MGKTDZCOTQGIDBUDW
BWYIFZTHDTJHYUEZN
KAPGEFREFAYADWNE
YRCIEOIXVUESESZ
ORVEOAOZDU
KMIVN

Since the prize is "swirling", I am guessing the letters are as well.

Image name is 388_meepitday.gif

Doubt it means anything, but you can pick out the words SKIRT, SHOT and BUD.

I think these are the correct letters:
GBWHGYW
OBUSKIRTXXEDYF
EOIUFKHYMGTJNCHR
VTSHOTAQZNCWNCBZ
MGKTDZCOTQGIDBUDW
BWYIFZTHDTJHYUEZN
KAPGEFREFAYADWNE
YRCJIEOIXVUESESZ
ORVEOAOZDU
KMIVN

hmmm... i like the 'swirling-letters' theory ... except neither of the Q's has a U anywhere around it.

i feel like there's going to have to be a substitution, but without spaces to denote words, internet cryptogram solvers are choking on it.