- #1
raminee
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- TL;DR Summary
- How to come up with an index for a set of number selections in combination theory
Hello All,
Not sure if this belongs in general math but lets start here and see where it takes us.
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter.
As an example , say we have digits 1 to 10. And we want to select 3 digits. A digit can not be repeated.
Combination theory tells us that there would be M! / ( (M-N)! * N! ). [ (!) means factorial]
So in this example we would get 10! / ( (10-3)! * 3! ) = 120 combinations of 3 different digit numbers.
Lets take the combination as an index indication of the 3 digits produced.
So if we have 120 possibilities then one could say :
digits 1,2,3 ==> index 1
digits 1,2,4 ==> index 2
digits 1,2,5 ==> index 3
---
----
digits 8,9,10 ==> index 120
My question or challenge is 2 folds:
A) Given 3 numbers how can one map it to one of the indices 1 to 120 ??
B) If an index is given how to recover the 3 digits mapped to this index ?
i.e. reverse of (A)
So to be clear I am looking for an algorithm that would define the process in A and B.
Thx
R.
Not sure if this belongs in general math but lets start here and see where it takes us.
In mathematics, a combination is a way of selecting items from a collection where the order of selection does not matter.
As an example , say we have digits 1 to 10. And we want to select 3 digits. A digit can not be repeated.
Combination theory tells us that there would be M! / ( (M-N)! * N! ). [ (!) means factorial]
So in this example we would get 10! / ( (10-3)! * 3! ) = 120 combinations of 3 different digit numbers.
Lets take the combination as an index indication of the 3 digits produced.
So if we have 120 possibilities then one could say :
digits 1,2,3 ==> index 1
digits 1,2,4 ==> index 2
digits 1,2,5 ==> index 3
---
----
digits 8,9,10 ==> index 120
My question or challenge is 2 folds:
A) Given 3 numbers how can one map it to one of the indices 1 to 120 ??
B) If an index is given how to recover the 3 digits mapped to this index ?
i.e. reverse of (A)
So to be clear I am looking for an algorithm that would define the process in A and B.
Thx
R.
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