Let the 4 lines be:
14, (91,961), 3
13, (161,692), 4
12, (251,443), 5
11, (361,214),6
Now add your line, which should be coherent with the logic of the 4 existing four lines.
(In reply to
re: solution please correct spoiler by Ady TZIDON)
I feel that my solution is as legitimate as yours.
The parenthesized values, treated as individual single numbers, do in fact form a quadratic function of an arithmetically increasing independent variable. In fact, only three such points are necessary to produce such a quadratic, and the fourth one actually confirmed the quadratic (as opposed to say cubic) nature of the function, as demonstrated by the equal second differences. This is in fact more reasonable than my solution to a previous puzzle that looked like this one, where I had to fit a cubic, with no real reason for doing so, as the numbers presented there did not themselves lead to any level of differences that showed equality; I had to assume it at the next level.

Posted by Charlie
on 20170611 10:04:49 