i have a list of 5 different numbers. the sum of 2 of the numbers is 0. the sum of 2 of the numbers is 1. the sum of 2 of the numbers is 2. the sum of 2 of the numbers is 3. the sum of 2 of the numbers is 4.the sum of 2 of the numbers is 5.the sum of 2 of the numbers is 6. the sum of 2 of the numbers is 7.the sum of 2 of the numbers is 8.the sum of 2 of the numbers is 9.the sum of 2 of the numbers is 10.the sum of 2 of the numbers is 11.the sum of 2 of the numbers is 12. what are the numbers?

please show how u got the answer

obviously we have

a -a b c d

Not much to do now but start guessing. If a=1, we have

1 -1 2 3 5 7 satisfies everything except sum=11

Gotta go for now. Maybe you can fill it in before I get back. :-(

To find the numbers, let's analyze the given information step by step:

1. The sum of 2 numbers is 0. To get a sum of 0, we need two numbers with opposite signs. Therefore, the list of numbers must include a positive number and its negative counterpart.

2. The sum of 2 numbers is 1. Again, to get a sum of 1, we need two numbers with opposite signs. Therefore, the list of numbers must include a positive number and its negative counterpart.

3. Following the same logic, the sum of 2 numbers is 2, so the list of numbers must include a positive number and its negative counterpart.

4. The sum of 2 numbers is 3. This time, the numbers cannot have opposite signs, as we need to get a positive result. Therefore, the list must include two positive numbers that sum up to 3.

5. Continuing, the sum of 2 numbers is 4. Again, we need two positive numbers to achieve this sum.

6. The sum of 2 numbers is 5. Here, we need a positive and negative number.

7. The sum of 2 numbers is 6. We need two positive numbers.

8. The sum of 2 numbers is 7. This time, we need a positive and negative number.

This pattern continues until reaching the sum of 12.

Based on this analysis, we can conclude that the list of numbers would be:
- One positive number and its negative counterpart (-n, n)
- Two positive numbers (m, o)
- One positive and one negative number (p, -q)
- Two positive numbers (r, s)
- One positive and one negative number (t, -u)
- Two positive numbers (v, w)
- One positive and one negative number (x, -y)
- Two positive numbers (z, aa)
- One positive number and its negative counterpart (-bb, bb)
- Two positive numbers (cc, dd)
- One positive and one negative number (ee, -ff)
- Two positive numbers (gg, hh)
- One positive number and its negative counterpart (-ii, ii)

Please note that we don't have specific values for the numbers, only their relationships to each other. So, the list would look similar to this:

(-n, n, m, o, p, -q, r, s, t, -u, v, w, x, -y, z, aa, -bb, bb, cc, dd, ee, -ff, gg, hh, -ii, ii)