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.
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 |
Solution
