My previous post on this https://jxsolberg.wordpress.com/2013/10/26/omg-its-factoids-on-factorials/ contained inexcusable errors. I will leave it up, for the comments mainly, but also to prevent being nagged to be the next Pope, since it amply demonstrates my Fallibility.
Ok, my mistakes were caused by confusing two separate processes:
1) Create a dictionary/ alphabetical ‘phone-book’ of all possible 4-letter words. (whether they make sense or not.) How many are there?
And 2) Given any handful of 4 letters, how many ways can they be re-arranged?
The second question was visually demonstrated in the ‘Factoid’ post with the little blocks lined up in rows. There were, and are, 24 ways to do it. The example I chose, P-O-S-and T, is particularly rich in ‘makes-sense’ combinations: 7 out of 24. Most randomly selected ‘trays’ have zero words spellable. And the number here, 24 is indeed 4-factorial, That is: ‘4X3X2X1’. End part two.
The first challenge is no less interesting(?) A truly heavy and worthless phone-book, its first entry will be ‘AAAA’, the second AAAB, and so on. And on and on. The last page will conclude with ‘ZZZZ’. perhaps appropriate for a book which took years to read. Get a life and go to sleep! in any order.
Of course the publisher is bugging me as we speak: ‘How many pages will there be?” I have to tell him ‘something’, so math to the rescue.
Well, there will be 26 X 26 X 26 X 26 words in the book. This is a result of the 26 letters in the English alphabet, and the process we use: choosing a first letter (26 choices), then a second, (also 26), and so forth.
The answer is 456,976 words. If we cram a hundred on a page, that’s 4,569 pages, with some empty space after ‘ZZZZ’. Makes War and Peace look like a ‘pamphlet’, it does. (That calculation, by the way is often written as 26^4.
Now, you could pick any entry and do the ‘letter-shuffle’ game with it, but as Bette Midler sang once ‘Why Bother?’ Yes, indeed, why bother, since anything you get by re-arranging is already in the list somewhere. You can look it up.
End of part one.
Ok, you ask, so what was that stupendous giant-stupid number you cited in the other post. Well, *hangs head* it was the number of entries in Volume Two of my best-seller series, the one with ‘All possible 24-letter words!’
The publisher is saying let’s wait on that, see how the first one sells. I kinda agree, since there are at present not enough trees in the galaxy to print even one copy of the behemoth.
Hope this clears up the matter, clears up what was the matter with my brain, and partially clears my MANE. Sorry, I MEAN NAME.. /JS