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One more line (Posted on 2017-05-10) Difficulty: 3 of 5
Examine the following triplets, find out the logic behind the arrangements and add another coherent line:

14; (3,431,961); 7
13; (5,121,692); 8
12; (7,291,443); 9
11; (10,001,214); 10

Your line: ……. N1;(N2);N3

Post a short comment about your process of solving.

See The Solution Submitted by Ady TZIDON    
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Some Thoughts trivial solution? -- or is this not the solution? | Comment 1 of 4
I say trivial in the sense that a cubic equation can be fitted to any four points.

At first I thought the middle entry, N2, was a set of three numbers, but then realized the commas are just the ordinary demarcation of groups of three digits in a large number, in this case, numbers running in the millions.

The N1 sequence is obviously decreasing linearly and N3 is increasing linearly. The only hypothesis I can think of is that the N2 sequence is part of a cubic sequence.

We need not find the actual equation, just finite differences:

3431961     5121692     7291443    10001214    13311005
      1689731     2169751     2709771     3309791
             480020      540020      600020
                    60000       60000
                    
                    
making the next line:

10; (13,311,005); 11

  Posted by Charlie on 2017-05-10 10:32:24
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