Correct.
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Go through each of the numbers, and count how many of them are odd. If you count an odd number of them, then their sum is odd. If you count an even number of them, then their sum is even.
13 is an odd number. Anything that cannot be evenly divided by 2 is an odd number. The number 13 also happens to be the sixth prime number which also makes it odd (strange in this case). The first few primes are 1, 3, 5, 7, 11, 13, 17, 23, 29, etc. These number have the strange property of of not being divisible by any whole number except 1 and itself. This also means that every prime number will also be odd.
You cannot do this, because you're taking odd numbers: if you add two odd numbers together, you will get an even number. Take the odd numbers in pairs, so you'll have 3 pairs plus an extra odd number. The 3 pairs make 3 even numbers. You can add up any number of even numbers and get an even number, so you will have an even + odd, which is odd. 30 is an even number, but your result will be odd, no matter what 7 odd numbers you choose.
Even numbers are divisible by 2 with no remainder. 13/2 = 6.5 so yes.
-13 is the number must you subtract from -13 to get a difference of 0