This is a tricky one.
We have an ordered set of numbers q, which can have any numbers in it
(no duplicates).
Example:
q = (1, 3, 4, 7, 12)
And we have a function f(x), which is defined as:
f(x) = x * 4 + 6
(written algebraically).
The question:
If you choose 4 different numbers from q, call them a, b, c,
and d:
What are the combinations of f(a) + f(b) that are algebraically
equivalent to the combinations of f(c) - f(d)?
That is, show all a, b, c, d for which this is true:
f(a) + f(b) = f(c) - f(d)
For the above q, we get this sample output:
f(1) + f(1) = f(12) - f(7) 10 + 10 = 54 - 34
f(1) + f(4) = f(12) - f(4) 10 + 22 = 54 - 22
f(4) + f(1) = f(12) - f(4) 22 + 10 = 54 - 22
f(1) + f(7) = f(12) - f(1) 10 + 34 = 54 - 10
f(4) + f(4) = f(12) - f(1) 22 + 22 = 54 - 10
f(7) + f(1) = f(12) - f(1) 34 + 10 = 54 - 10
f(3) + f(3) = f(12) - f(3) 18 + 18 = 54 - 18
The left column shows the a-d inputs to f(x), and the right column
shows the result from the what f(x) returns for each of those.
No test script for this one. Keep in mind your output might be in a different order than the above.