Well I'm sorry but I didn't go far enough into my calculation... but the answer that I come up with now is...
So the answer would be...
7 * 120 = 840 * 21 = 17,640 * 1 = 17,640
I stand corrected
On the subject of prime numbers that satisfy the conditions, on my two hour round trip to the eye doctors I just thought of a much better way to explain it.
First of all, they want all the prime numbers that when we add one to them make a perfect square. If we let P be the prime number an X be the root of the square number, we get the following:
P + 1 = X^2
Let's isolate the P term.
P = X^2 - 1
Now let's use the reflexive property to eliminate the P variable
X^2 - 1 = X^2 - 1
As we all know, any integer when squared yeilds a perfect square. We also know that 1 is a perfect square. With these fact, we notice we have the difference of squares.
X^2 - 1 = (X + 1)*(X - 1)
This is a mathmatical proof which states that one less than the square of any term is equal to the product of one greater than and one less than the term.
Using our substitution property, we can then form the equation:
P = (X + 1)*(X - 1)
Since the definition of a prime number is any number that is divisible by only 1 and itself, we can conclude that the terms (X + 1) and (X - 1) must be equal to 1 and P for our P to remain prime.
If: X + 1 = 1
then: X = 0
yields: P = -1.
If: X - 1 = 1
then: X = 2
yields: P = 3
The possible values for our Prime number are -1 and 3, but since -1 does not fit in the range of 1 to a million (plus negatives are technically not prime numbers) we can conclude that 3 is the only possible prime number that fits the description.
Okay okay, so that looks rather complex. But for all you mathematitions out there, you should be able to understand why 3 is the only number that works if you can convince yourself to get to the step concerning the difference of squares.
And as for the Food Chia list.. ^^' I thought that "Durian" was "Darigan". >.> that's why I forgot to count it.
But anyway, you all can work it out for yourselves!
Prime + 1 = Squared
Prime = Squared - 1
There you go, a difference of squares. And now it's pretty easy for you to calculate without reading my incomprehensible ramble.
And thank you Eliz for correcting my misconception about fact 3. ^^' It was a bit of a trial and error phase.
But I was thinking in the long long car ride and realized that my 4th rule, the one for numbers ending in 0, worked for all numbers. Then about 3 seconds later I had the proof done in my head and have been eager for nearly 100 minutes (hour 40 minutes) to get here and put it up.
Well I messed that one up because of
durian. Otherwise I have a feeling I may have been in the first 200.
Dern durian/darigan...
Isfan wrote:Dern durian/darigan...
I'm only familiar with that term because my son's math curriculum is Singapore Math, and that's one of the fruits they use in their word-problem examples. Apparently it's fairly common out in southeast Asia.... :wink:
Eliz.
When it comes to very big numbers and figuring put mulitiple problems in math, there tends to be a HUGE chance that the answer will be off. I know that for a fact. and so, as many epople (espacially teachers) say, double-check your work. Just a reminder.
Just to put a line under the theory behind the prime numbers... I picked up a list of all primes between 1 and a million (there are less than 80,000 of them) from
http://www.rsok.com/~jrm/printprimes.html (actually d/l'oaded their program and ran it at home), and used a couple of little excel tricks to do a brute force check.
Indeed 3 is the only prime number between 1 and a million that will satisfy the condition... So... Is tehre a consensus on the number of food colors and TCG cards yet? I've heard 21 and 120... Shall we assume these to be correct? Any other takes on these 2 numbers?
lem wrote:So... Is tehre a consensus on the number of food colors and TCG cards yet? I've heard 21 and 120... Shall we assume these to be correct? Any other takes on these 2 numbers?
21 is the number of "food" colours a chia can be painted... and 120 is the # of cards in the TCG set... check out what isfan wrote.. included the link for proof.
Yes, but remember that it says "the number of prime numbers from one to one million blah blah" so there is only one prime number..... they got me on that one..... i guess no 200nps next week.... v.v
a Durian is a food, its spikey with some things inside that you eat.
Well there are 7 shops in Brightvale, right?
so 7 x 120 x (um, let's see. I'm looking at the rainbow pool right now. Apple, Asparagus, Aubergine, Avacado, Blueberry, Carrot, Chocolate, chokato, Durian, Gooseberry, Grape, Lemon, Lime, Orange, Pea, Peach, Pear, Pineapple, Plum, Thornberry, and Tomato. Wait, is a Thornberry a food? well it sure looks like one. If you count the thornberry as a food and Durian as a food, then thats....21.)
7 x 120 = 840.
840 x 21 = 17640.
17640 x 3 = 52920.
Is this the answer? Does anyone agree with me? I don't even know if I agree with myself, considering lack of skill in math.
I bet you all that there is something big that we all overlooked, like an unlisted color of "food" chia. And then once only like 20 people win the conundrum, everyone will be mad because they didn't think of it. I jsut have a feeling. Maybe I'm wrong though. hmmm.
17640 x 1 = 17640. sorry! Like I said, I don't even know whether to agree with myself.
look you cant muliply by 1... any maths book will tell you that 1 is technically not a prime number as it can only be divided by one which is its self so it must be the previous answer when it was multiplied by 3!! otherwise it doesnt satisfy neopets requirements.... it is the one which is 7 x 21 x 120 x 3 = 52920
trust me ive done enought on rational irrational real and prime numbers to know!
for those that dont get it
THE ANSWER IS 52920
satanonholiday wrote:any maths book will tell you that 1 is technically not a prime number
I don't think anybody is claiming that "1" is a prime number.
In any case, the question doesn't say to multiply by the prime number with the given properties, but by the
quantity of primes with those properties. And there is only one prime (the number "3") with those properties. Since you're supposed to multiply by the quantity of primes ("one") and not the actual primes ("three"), using "1" in the product is indeed correct.
I cannot speak to the accuracy of the other numbers.
Eliz.
So, here's the list:
7 shops
120 cards
21 chias
1 prime number
7 x 120 x 21 x 1 = 17640.
Yeah, pointing to the fact that it is actually just saying one prime number, not necessarily one is the one prime number...Yeah, you're prob gona now think 'Yeah you didn't need to say that, we had realised, stop being a stupid b****....' but just for anyone who was a bit confuzzed...
THE AWNSER
The Neopets Staff [theneopetsteam]
Sent: 25/5/2005 10:35am
Subject: Congratulations!
Folder: Inbox
Message:
[Report Message] Congratulations! You have guessed correctly in the Lenny Conundrum game (Round 117). We have given you 1613 NP!
yes everyone it was 17640.
