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Love the problem!
Just a couple of twisted thoughts.
Given a set of data, our first move would be to apply a set of operators to the independent variables, such that the result equals the dependent variable for one line of input data.
Then we apply the formula to the following lines of input, one after another until we get a set of data that fails.
Having successfully negotiated all of the given data, do we assume (yes yes I know) the formula isthe correct one? Or do we need to attempt to find all (sigh) possible formulas that will work out when applied to the data set?
Either way we are left with the sticky problem of trying to know all possible fomulae that will solve a given set of data for a given set of answers. This begins to smack of cryptography.
Some series may not play fair such as:
would the following fit in as a possible data set?
1 4 1 3
"formula" to get x,y and z needs to be blown out for each value.
Thanks for a fun problem and headache! Good luck.