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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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Solution Solution Comment 5 of 5 |
I tried this without looking at any prior answers.

For N2, I tried various base changes, but that led nowhere.
Then I noticed the first 3 (or 4) digits of N2 were perfect cubes.
When I started splitting N2 into 3 groups, I hit success.

Here are the next few lines:
10; (13311005); 11
9; (1728816);   12
8; (2197647); 13
7; (2744498); 14

Explanation:
Let's rename the first number (N1) as 'i'.  And then (N3) = 21-i
Then the 3 parts of N2 are:
(21-i)^3  ,  i^2  ,   15-i

N1=i    |------(N2)------|     N3
20   1   400   -5   1
19   8   361   -4   2
18   27   324   -3   3
17   64   289   -2   4
16   125   256   -1   5
15   216   225   0   6
14   343   196   1   7
13   512   169   2   8
12   729   144   3   9
11   1000   121   4   10
10   1331   100   5   11
9   1728   81   6   12
8   2197   64   7   13
7   2744   49   8   14
6   3375   36   9   15
5   4096   25   10   16
4   4913   16   11   17
3   5832   9   12   18
2   6859   4   13   19
1   8000   1   14   20
0   9261   0   15   21

Edited on October 9, 2020, 11:18 am
  Posted by Larry on 2020-10-09 11:16:51

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