The number of shops in Brightvale is 7. You can find this just by going to the map and counting them.
Brightvale: 7
The TCG collection has 120 cards in it. If you don't believe me go here:
http://www.neopets.com/tcg/checklist.phtml?edition=7
TCG: 120
The number of Chia food paints is 20. Count them yourself here:
http://www.neopets.com/rainbowpool_allpetcolours.phtml?get_pet=Chia
(Dont forget that Orange is a food color.)
Chia: 20
Here's the tricky part. all the prime numbers from one to a million that when you add 1 to them become a perfect square.
To do this step I had to work backwards.
First I took numbers, squared them, and then subtracted one to see if they were prime. Here's what I quickly learned:
1. Any odd number (a number that ends in 1, 3, 5, 7, or 9) when squared yeilds an odd number, and when you subtract 1 from an odd number it becomes even, and even numbers are not prime.
2. Any number ending in 4 or 6 would not work, because when you square then your units digit will always be 6, subtract one and you get 5, and anything ending in 5 (excluding 5) is not a prime number.
3. Any number ending in 2 or 8 when squared and had 1 subtracting from it is always divisible by 3. Don't ask me why, but just try it yourself. Pick any big number ending in 2 or 8 (like 55552), square it, subtract one, and divide by 3. You'll see that it always works.
With this, I knew that all numbers ending in 1, 2, 3, 4, 5, 6, 7, 8, or 9 did not work.
This just left me with the number 0.
This part is a little tricky:
4. When a number is divisible by 10, if you square it and subtract 1, the product you get from this is always divisible by the your initial number plus and minus 1. (I.E. 10 squared yeilds 100, minus one yeild 99. 99 = 9 * 11, therefore it is not a prime number.) As you can see, 10 yielded 99, which is the same thing you would get if you took (10 - 1)*(10 + 1). Try it with any number, really.
With these fact we can determine no two digit number can be squared then have one subtracted from it to yield a prime number, though there may be exceptions to these rules if we go down into the single digit numbers. So we check.
1) 1 is technically not a prime number, but it still doesn't work. 2 is not a perfect square.
2) Two is the only even prime number, but unfortunately 3 is not a perfect square.
3) three plus one yields four, which we all know is 2 squared.
So there is at least 1 prime number between 1 and a million that fits the description we need. This means our answer wont be zero. Let's quickly check the rest of the primes below 10.
5) 6 isn't a perfect square.
7) 8 isn't a perfect square.
That's all the single digit prime numbers. So between 1 and a million, only the number 3 when adding 1 to it makes a perfect square.
Primes: 1
We tally up the totals:
Shops: 7
TCG: 120
Chia: 20
Primes: 1
7 * 120 * 20 * 1 = 16800.
And that's your answer.
I'm trying to find out how many cards are in the curse of maraqua tcg set at the moment...
that's great... all the info I can find on neo just shows like, 4 booster packs, and says they contain 8 cards each... so at the moment I'm assuming 32... but I know diddly about how the TCGs work 