>>>>>Bruce, I didn't use combinatorics to find solution. There is another purely algebra method to do this.
>>>>
>>>>It's probably easier, too. My training has me using combinations/factorials as a medium for deriving solutions for this type of problem, but it's certainly not always the best/easiest way. Though the fastest way may be to guess the solution and use induction to show it works :~)
>>>
>>>In math analysis, this problem is actually finding a line crossing 4 points.
>>
>>Ah, like best-fitting a polynomial?
>
>Yes!

That's how I got my answer, sort of.

I graphed it and recognized that I was dealing with a polynomial. So I started by graphing y=x^2 and worked from there. I guess Edward's method was better than mine. I cheated using Excel. It's been years since high school.....