What are four consecutive numbers that add up to 4?

Answer 1

There are no four consecutive integers whose sum equal four. For example:
1 + 2 + 3 + 4 = 10
0 + 1 + 2 + 3 = 6
-1 + 0 + 1 + 2 = 2
-2 + -1 + 0 + 1 = -2
...
and so on.

On the other hand, if you want to use a very loose definition of consecutive, there are four non-integer values that are each one apart and whose sum equals 4. You can calculate them like this:

x + (x + 1) + (x + 2) + (x + 3) = 4
∴ 4x + 6 = 4
∴ 4x = -2
∴ x = -0.5

so the numbers would be:
-0.5, 0.5, 1.5, 2.5