What do you mean by "inverted the position of two of those words, two times"? How exactly you did that will affect the number of possibilities (as some orderings could be ruled out).
The upper bound to this is (24 choose 4) * 4! = 255024. (24 choose 4) is the number of ways you can choose 4 items from a set of 24 elements. 4! is the number of ways you can order those 4 elements. This is a multiplication since for each way you can choose 4 items, there are 4! ways you can rearrange them.
Let's say the seed is:
Word1 Word2 Word3 Word4 Word5 Word6 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word19 Word20 Word21 Word22 Word23 Word24
Well, my "encryption" technique was to write in that order:
Word1
Word23 Word3
Word21 Word5 Word6 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word19 Word20
Word4 Word22
Word2 Word24
So I switched Word2 <> Word23 and Word21 <> Word4
But when I try to revert that, this doesn't work. So I must have screwed up somewhere. My hypothesis is that I have inverted the "wrong" words, but I don't know which ones.
The inversion should have been made in a symetrical position, like in my example.
But since I screw up, maybe I have switched words in a non symetrical position.
I know I'm late to the party with Coding Enthusiast showered with merits. I hope he helped you get your key back, because if he didn't :
I don't see how there are that many combinations unless he bruteforced every possible permutation of 4 from 24, which is roughly 331776 possibilities (minus repetitions I guess.)
If I strictly follow the way you switched up your words :
You swap every word with its symmetrical other word.
You swap exactly 2 words.
This will HUGELY reduce the number of possibilities, but don't take my word for it :
http://jsfiddle.net/gu2809ht/I wrote this in 5 minutes and didn't bother to make an output in html (sorry), so press run and open your console and you'll see the output :
Word24 Word23 Word3 Word4 Word5 Word6 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word19 Word20 Word21 Word22 Word2 Word1
Word24 Word2 Word22 Word4 Word5 Word6 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word19 Word20 Word21 Word3 Word23 Word1
Word24 Word2 Word3 Word21 Word5 Word6 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word19 Word20 Word4 Word22 Word23 Word1
Word24 Word2 Word3 Word4 Word20 Word6 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word19 Word5 Word21 Word22 Word23 Word1
Word24 Word2 Word3 Word4 Word5 Word19 Word7 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word18 Word6 Word20 Word21 Word22 Word23 Word1
Word24 Word2 Word3 Word4 Word5 Word6 Word18 Word8 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word17 Word7 Word19 Word20 Word21 Word22 Word23 Word1
Word24 Word2 Word3 Word4 Word5 Word6 Word7 Word17 Word9 Word10 Word11 Word12 Word13 Word14 Word15 Word16 Word8 Word18 Word19 Word20 Word21 Word22 Word23 Word1
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The number is so small because symmetrical swapping reduces in half the number of permutation, (1<>24 is the same as 24<>1). The list above is exhaustive of every possible way you can permute using your special technique.
I just couldn't help comment in case you still didn't try to import/test the 30 thousand possibilities, I hope you don't have to
In case you're not sure you swapped them symmetrically of course, you can expand the search radius, but there are a few steps before trying the full 30k solutions. (Like if the 2 words you swapped were neighbors, or far away by n words, etc.. which are also much less)
I'm also as jealous as a middleschool schoolgirl because this is a really easy problem.. Right place at the right time I guess