by Smythe Dakota » Fri Oct 13, 2017 3:14 pm
That's why, even though I'm a math person, I have always hated those "what's next in sequence" puzzles. There are often multiple reasonable answers, even if you don't go as far outside the box as I did!
In fact, given any N points (1,y1), (2,y2), (3,y3), ... (N,yN) on a coordinatized xy-plane, there always exists an (N-1)st degree polynomial (expressing y as a polynomial in x) that goes through all N of the given points. Just find that polynomial, and plug in N+1 for x, and bingo, you have the next element in the sequence.
Going further, if we change "(N-1)st degree" to "Nth degree", now there are infinitely many such polynomials, and any answer qualifies as a legitimate "the" next element in sequence.
Bill Smythe