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Shifting Alphabets; How can I PROVE this rule?
Topic Started: Sep 28 2005, 03:39 PM (416 Views)
Revelation Sep 30 2005, 12:35 PM Post #16
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 Well, the ! means the number of solutions for a normal swap.

With two number:
AB - BA : 2

Three:
ABC - ACB - BAC - BCA - CAB - CBA : 6

This is simply calculated by the length n, multiplied by n-1, n-2 etc.

So with a length of three it would become 3 * 2 * 1 = 6 possibilities.

e is a constant value used in difficult math problems and somehow this works. I will ask someone later today about that. Maybe this will help.
RRRREJMEEEEEPVKLWENFNVJKEEEEEAOLKAFKLXCFZAASDJXZTTTTTTTLSIOWJXMOKLAFJNNKFNXN
RAGRBAQEMHIGDJVDSEOXVIYCELFHWLELJFIENXLRATALSJFSLCYTKLASJDKMHGOVOKAJDNMNUITN
RRRRLJVEEEEECLYVYHNVPFTAEEEEEMWLMEIRNGLARWJAKJDFLWNTIERJMIPQWOTZEOCXKNUBNXCN
RJIRPOWEANFUSNCZVDVZNMSFEKLOEPZLDKDJWSAAAAAAAOERHJCTNCKFRIMVKSOFOMKMANREWNBN
RZUDRGXEEEEENFQIDVLQNCKNEEEEEDGLLLLLLAWIOSNCDARLODMTOEJXMILDFJROTKJSDNLVCZNN
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Donald Sep 30 2005, 12:50 PM Post #17
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Quote:
 
e is a constant value used in difficult math problems and somehow this works.

Very interesting. I'm familiar with "e", I just wouldn't have assumed it had any connection to this problem, and still don't quite understand how it does. I am axiously awaiting your friends answer!
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insecure Sep 30 2005, 03:08 PM Post #18
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 I don't see it either, Donald.

If it's any help, n! is certainly the number of possible keys n distinct characters in length.

I'm not sure how dividing by e helps, though.
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Revelation Sep 30 2005, 06:57 PM Post #19
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 Well, e is the basis of a natural logarithm. Mathematicaly seen e is the limit of the set 1 + 1 + 1/2! + 1/3! + 1/4! + ... + 1/n!
RRRREJMEEEEEPVKLWENFNVJKEEEEEAOLKAFKLXCFZAASDJXZTTTTTTTLSIOWJXMOKLAFJNNKFNXN
RAGRBAQEMHIGDJVDSEOXVIYCELFHWLELJFIENXLRATALSJFSLCYTKLASJDKMHGOVOKAJDNMNUITN
RRRRLJVEEEEECLYVYHNVPFTAEEEEEMWLMEIRNGLARWJAKJDFLWNTIERJMIPQWOTZEOCXKNUBNXCN
RJIRPOWEANFUSNCZVDVZNMSFEKLOEPZLDKDJWSAAAAAAAOERHJCTNCKFRIMVKSOFOMKMANREWNBN
RZUDRGXEEEEENFQIDVLQNCKNEEEEEDGLLLLLLAWIOSNCDARLODMTOEJXMILDFJROTKJSDNLVCZNN
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insecure Oct 1 2005, 06:21 AM Post #20
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 Yes, I know. By the way, we say "base" rather than "basis" when talking about logarithms. That is, e is the base of natural logarithms.

(I bother to correct your English only because it is already so good. If you were useless at English, I wouldn't see the point!)

You see, the problem is not that Donald and I don't know what e actually is. We do. The problem, rather, is that we don't see why it applies here. What significance does n! / e actually have? What does it tell us, and why?
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Revelation Oct 1 2005, 08:06 AM Post #21
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 Thanks for the correction :)

Say s_{n} is the number of 'good' combinations for n letters. Then you'll get this:

s_{n} = (n-1)*(s_{n-1} + s_{n-2})

Table:
============
n ............... s_{n}
1 ............... 0
2 ............... 1
3 ............... 2
4 ............... 9
5 ............... 44
6 ............... 265
7 ............... 1.854
8 ............... 14.833
9 ............... 133.496
10 ............. 1.334.961

You see that for n=10 s_{n} is 1.334.961. But 10!/e is also 1.334.961! So n!/e also does the trick.

The formula can also be written as s_{n} = n*s_{n-1} + (-1)^n, which is Euler's formula.
RRRREJMEEEEEPVKLWENFNVJKEEEEEAOLKAFKLXCFZAASDJXZTTTTTTTLSIOWJXMOKLAFJNNKFNXN
RAGRBAQEMHIGDJVDSEOXVIYCELFHWLELJFIENXLRATALSJFSLCYTKLASJDKMHGOVOKAJDNMNUITN
RRRRLJVEEEEECLYVYHNVPFTAEEEEEMWLMEIRNGLARWJAKJDFLWNTIERJMIPQWOTZEOCXKNUBNXCN
RJIRPOWEANFUSNCZVDVZNMSFEKLOEPZLDKDJWSAAAAAAAOERHJCTNCKFRIMVKSOFOMKMANREWNBN
RZUDRGXEEEEENFQIDVLQNCKNEEEEEDGLLLLLLAWIOSNCDARLODMTOEJXMILDFJROTKJSDNLVCZNN
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PulsarSL Oct 2 2005, 11:48 PM Post #22
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Revelation
Oct 1 2005, 08:06 AM
Thanks for the correction :)

Say s_{n} is the number of 'good' combinations for n letters. Then you'll get this:

s_{n} = (n-1)*(s_{n-1} + s_{n-2})

Table:
============
n ............... s_{n}
1 ............... 0
2 ............... 1
3 ............... 2
4 ............... 9
5 ............... 44
6 ............... 265
7 ............... 1.854
8 ............... 14.833
9 ............... 133.496
10 ............. 1.334.961

You see that for n=10 s_{n} is 1.334.961. But 10!/e is also 1.334.961! So n!/e also does the trick.

The formula can also be written as s_{n} = n*s_{n-1} + (-1)^n, which is Euler's formula.

interesting...
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