FURTHER COMMENT ON THE PUZZLE

The real mathematical answer, of course, is that every answer is correct!  Any finite string of integers is compatible with an infinite number of next integers, each one according to some formula or other.  That is the thing about these questions on intelligence exams that always bugged me, sixty-five years ago when I was still taking them.  IQ tests were all the rage when I was in grade school.  Natie Gold scored 169, which was supposed to mean that he was a genius.  The cleverest thing I ever saw him do was rig a cigarette lighter on the end of a water pistol and fill the water pistol with lighter fluid, making the whole contraption a quite acceptable handheld flame thrower.  He was a chubby little kid.  I wonder what ever happened to him.  P. S. 117, back in the middle '40s.  I don't suppose anyone reading this knows.