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Is there a way to find the relation between numbers? I have 2 groups of numbers.

Group A

5 --> 20
6 --> 32
7 --> 112
8 --> 192
9 --> 576
10 --> 1024

Group B

7 --> 56
8 --> 80
9 --> 432
10 --> 672

Is there a way to find relation between numbers and if there's no way to do that except mentally, what is the relation in the two groups?

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Unfortunately, there is often no definitive way to determine a pattern within some given set of numbers, since patterns may be as arbitrary as you like. However, there are some ways of seeing patterns a little more clearly.

By way of example, I'm going to rewrite these relations in a slightly different way. Using that as a hint, try and find the relations yourself. I'll place the answer in a spoiler below.

Group A:

$5\to 2^2\cdot5$

$6\to 2^5$

$7\to 2^4\cdot7$

$8\to 2^6\cdot3$

$9\to 2^6\cdot9$

$10\to 2^{10}$

Group B:

$7\to 2^3\cdot7$

$8\to 2^4\cdot5$

$9\to 2^4\cdot3\cdot9$

$10\to 2^5\cdot3\cdot7$


Group A:

When $n$ is odd, $n\to n2^{n-2}$. When $n$ is even, $n\to2^{n-3}(n-2)$

Group B:

When $n$ is odd, $n\to 2^{n-6}\cdot n(n-3)$. When $n$ is even, $n\to 2^{n/2}(n-3)(n-7)$

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  • $\begingroup$ thank you, jazzy. i have found a relation for all numbers in group a it's 2^n-3 (n-2+2(n mod 2)) but isn't there such one for group b without separating odd and even . $\endgroup$ – user3767289 Mar 14 '17 at 7:39
  • $\begingroup$ oh i found one for group b too : 2^((n-6(n mod 2)) / (-(n mod 2)+2)) x (n-7 + 7(n mod 2)) x (n-3) it's a bit long but it works . thanks $\endgroup$ – user3767289 Mar 14 '17 at 8:02
  • $\begingroup$ If the equations are going to get that complicated, you might as well lagrange group B to get f(x)=−(220x^3)/3+1924x^2−49328x/3+46032 which is actually shorter than what you had... i think. $\endgroup$ – Wen1now Mar 14 '17 at 8:43
  • $\begingroup$ I don't like the answer for B. You are splitting it into 2 sequences, which means you only have 2 samples for each, which isn't enough to determine a relation. You might as well just do a linear equation, so odd= 188n-1260 and even= 296n-2288 $\endgroup$ – Kruga Mar 14 '17 at 8:55
  • $\begingroup$ I agree that it's a little fishy since there are so few samples. I feel that the answer to Group B suffices due to the context given by group A, though certainly I'm sure that there are more than a few distinct solutions because the given sequence is so short. $\endgroup$ – Santana Afton Mar 14 '17 at 9:00

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