Finally! The truth about four-letter words, etc.

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.
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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.
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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

OMG! It’s Factoids on Factorials!

Again, whistling in the WP Darkness, I’m sure you are all curious just how many combos of any four letters there are.
Well, there’s a formula, you can look it up, but we don’t need no stinking formulae! We just spend an hour making a nifty chart (above…can’t put stuff where you want it here, ugh!)

Look at it this way: There are four choices for the first letter, (The four quarters of the chart)

And once that letter is chosen, there be three choices left to explore for the second letter in the ‘word’.
And finally, the remaining two letters can appear in any of two different orders.
Putting it together, there are four (4) times three (3) times two (2) possible letter orders. Dat’s 24 and in math, 24 is called the ‘factorial’ of 4, and written as   ‘4!’   Yes with an exclammation mark! As in “Oy, I’m just so freaking happy I read this post!‘

Three-letter words, by extension, have only 6 possibilities (3X2X1)
And when we presently tackle FIVE-LETTER WORDS! there will be 120 choices for each scrabble-tray of 5 letters. Yes, 5! equals 5X4X3X2X1 =120. We always mention the ‘one’ at the end, so he don’t feel left out. and dat’s the story here…
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Almost.
“So”, you’re asking, “how many possible four-letter words could there be in English?”
‘You mean, if they don’t have to make sense?’
“Yeah, most of the popular ones I think I’ve heard already.”
Ok, the answer is simple. It’s 24! (twenty four factorial, that is!)
A big number, and by coincidence(?) very close to another whopper, Avogadro’s Number. It’s about 6 followed by 23 zeros! Even if you spent your lifetime spewing four-letter words you’d hardly get started before they buried you, still cursing bitter Fate.
We can figure this one out too, while we’re crunching digits. At one ‘expletive-deleted’ per second, working 24 hours X 60 minutes X 60 seconds, you’d blabber 86,000 words a day. That wouldn’t even get you  to the ‘F-U’s, and I’m guessing that you’d go to your Maker trying to cheat, screaming ‘FART on a RAFT, I HATE Factorials!’

Perhaps if you’d read this post first, you would have reconsidered your dream.

   Since I don’t have any real problems of my own, as I drive around at 4 o’clock in the morning through the hills of Samaria in a less-than-totally-festive Ford Fiesta, with half a ton of lumber sticking out 3 feet forward and four feet rearward, hoping I didn’t forget any critical tools, (I did), or materials (ditto), wondering whether drinking my lunch already would be considered de-classe… I invent problems. Here’s the one I used to keep my mind off my “It’s a Beautiful Life” this morning.
     In a mixed-up little country far away, a well-meaning poor-soul in the above situation comes to a grisly halt on the side of the road. No amount of optimism can weigh in against the grim truth: “Your car is Dead… Oh, and so are you, haha!” Accepting his fate, he starts walking. Around the bend in the road he comes to the following sign:

   Turning around, he trudges dejectedly back, past his dead car, in the opposite direction, and finally comes to another sign. Same message! An hour later, on a seemingly hopeful gravel road, he finds the exact same sign, obscured somewhat by acacia trees and twenty-year-old election campaign stickers. Using the last miliwatts of his cell-phone’s battery, he learns from the infinitely brainless and impatient tow-truck goon only that he needs to know where he is, first. “I kinda knew that! But thanks anyway, asshole.” he thinks to (what’s left of) himself. Now assuming Accuracy-in-Signage, he’s got an interesting math problem on his hands, among other problems. Setting aside conveniently the fact that “too far to walk” is a highly relative term, he assumes that if it’s like 20 kilometers to Dumbville, then of course it’s 40 to Dumberville. And whatever distance is referred to by the additional signs, the true part of their message is that it’s exactly twice as far to Dumberville. Every sign was put there, thoughtfully, by trained surveyors, precisely at a point where the relative distances are as advertised. Quickly building a table (with attached shade-trellis) and a comfortably utilitarian chair from the now-doomed lumber on the roof rack, he sets out to tackle this possibly soluble problem first, before moving on to more intractable challenges. His goal is none other than to determine, from the relative locations of the three signs, where he is.. or to prove that this is impossible. We now go to MSPaint, where anything is possible.

And of course, I could have simply asked “What is the set of points C1, C2, C3….. on a plane surface, such that each point is exactly half as far from arbitrary point A as it is from arbitrary point B?” But that wouldn’t have been as much fun. Unless, as I’m starting to believe, I have a weird idea of what’s fun.