Congratulations! You have guessed correctly in the Lenny Conundrum game (round 204). You have won 243 NP!
Because you were in the first 250 to guess correctly, you also have been awarded a Scrambled Egg on Toast, and receive a trophy and the Lenny Conundrum avatar!
There is nothing really tricky about it. You just need to know how many numbers between 1 and 1000 inclusively that have an odd number of divisors. A number n can be writting in canonical form:
n = p1^(a1)*p2(a2)*p3(a3)...pr(ar), where each pi is a distinct prime.
the number of divisors of n is simply the product:
Nd =(a1+1)(a2+)...(ar+1), since each ai can take on the value 0,1,...,ai.
Hence for n to have an odd number of divisors Nd must be odd. This will only be true iff each ai is even (for if an ai is odd Nd will be even) thus n is a perfect square (n = k^2). So find and integer such that s^2 <= 1000. We find s = 31. So there are 31 positive integers less than 1000 that have an odd number of divisors.
Hope this helps. I LOVE NUMBER THEORY!
ummmmm
uhhhh ummmm *drools* A little too much THC in the brain to understand that at the moment
Yeah, I agree. I don't understand that at all, I usually come here for the answers
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The answer is 31.
1X1 = 1 (open)
2X2 = 4 (open)
3X3 = 9 (open)
4x4, 5x5, 6x6, ect. It can only go up to 31. The pattern is easy to see.
anyone know the mystery pic answer for this week or know where i can get
Yay!
I got the neomail for answering correctly this week.
But it was only about 500 neopoints.
xD
When does the next competition start?
Later today or early tomorrow?
Dear Princess,
Congratulations! You have guessed correctly in the Lenny Conundrum game (round 205). You have won 584 NP!
Yours Sincerely,
The Neopets Team!
I am awaiting the next new Lenny also. Gee I hope it's an easy one:)
Good Luck 2 One & All!
New Comundrum is out!! Has anyone checked it out yet?
Remnok the Nomad has a brother, Damon the Nomad, who's fond of coming up with math puzzles. Anyway, he came up with one that uses his own name:
Assume each letter in the following formula represents a unique digit: (for example, ABCD could be the number 1234)
NOMAD x 4 = DAMON
What is the number represented by the digits DAMON?
Well, I noticed that DAMON is the palindrome of NOMAD.
Anyone have any ideas on this one? I am lost!
This looks like Nomad spelled backwards make Damon. I don't understand what digit are they referring too?
The number must be the same forward as backwards and be divisible by 4
candi5757 wrote:This looks like Nomad spelled backwards make Damon. I don't understand what digit are they referring too?
Yes, that's what a palindrome is. The backwords spelling of a word.
Also each digit must be unique!
Now I am totally lost.
D x 4 =
A x 4 =
M x 4 =
O x 4 =
N x 4 =
Am I on the right path? Please help!
