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# HELP

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There are 4! (or 24) "words" that can be formed using each of the letters a, b, c and d once. If these "words" are alphabetized, which one is 17th?

Jul 6, 2018

#1
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{a, b, c, d} | {a, b, d, c} | {a, c, b, d} | {a, c, d, b} | {a, d, b, c} | {a, d, c, b} | {b, a, c, d} | {b, a, d, c} | {b, c, a, d} | {b, c, d, a} | {b, d, a, c} | {b, d, c, a} | {c, a, b, d} | {c, a, d, b} | {c, b, a, d} | {c, b, d, a} | {c, d, a, b} | {c, d, b, a} | {d, a, b, c} | {d, a, c, b} | {d, b, a, c} | {d, b, c, a} | {d, c, a, b} | {d, c, b, a} (total: 24)

cdab is the 17th permutations.

Jul 6, 2018
#2
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There are 4! (or 24) "words" that can be formed using each of the letters a, b, c and d once.

If these "words" are alphabetized, which one is 17th?

sorted:
$$\begin{array}{|r|r|} \hline 1. & abcd \\ 2. & abdc \\ 3. & acbd \\ 4. & acdb \\ 5. & adbc \\ 6. & adcb \\ 7. & bacd \\ 8. & badc \\ 9. & bcad \\ 10.& bcda \\ 11.& bdac \\ 12.& bdca \\ 13.& cabd \\ 14.& cadb \\ 15.& cbad \\ 16.& cbda \\ \color{red}{17.} & \color{red}{cdab} \\ 18.& cdba \\ 19.& dabc \\ 20.& dacb \\ 21.& dbac \\ 22.& dbca \\ 23.& dcab \\ 24.& dcba \\ \hline \end{array}$$

Jul 9, 2018
edited by heureka  Jul 10, 2018
#3
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heureka:

There is some discrepancy between your permutations and those of the "Guest" in alphabetical arrangements.

Notice that the first permutation is "abcd" and the last one must be the "exact reverse" of the first, namely, "dcba".

Jul 9, 2018
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Mr. BB, the discrepancy is only in your head. ...I’m not sure how you noticed this in all the mind clutter. .

Heureak’s algorithm stopped sorting after finding the 17th alphabetical permutation. There is no reason to sort any more for this question. In fact, there is only a need to sort two to find the 17th alphabetical permutation. There is no need for a computer, either.

Logically, from inspection, the first eighteen divide into groups of six starting with A, B, and C. The eighteenth is CDBA, and the alphabetical permutation preceding this is CDAB.  See, simple logic via brainpower.

Now your computer is free to do a complex task, such as analyzing whether Banana Peel or Peanut Shell will win the steeplechase. My computer said Banana Peel, but he slipped and came out forth.

.

GA

Jul 9, 2018
edited by GingerAle  Jul 9, 2018
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Who is Mr. BB you ape face? I noticed that by comparing them alphabetically because once you program a computer to print all the permutations in alphabetical order, it continues in that order until the end, if it is programmed correctly. That is all Miss "brainpower". By the way, who made the spokesperson for Mr. heureka?

Jul 9, 2018
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Usually Mr. BB is the Blarney Banker. He nitters about trivial, irrelevant inconsistencies in posted solutions –usually on Heureak’s posts. You also nitter about trivial inconsistencies.

In your case, Mr. BB stands for Bullshit Bug, because you are reminiscent of a dung beetle. The analogy is limited though, because dung beetles are useful and fascinating creatures, while you are neither.

I noticed that by comparing them alphabetically because once you program a computer to print all the permutations in alphabetical order, it continues in that order until the end, if it is programmed correctly.

Well, that is exactly what it did, so it’s programmed correctly.  It continued to sort, by groups of six, on A, B, and C until the end. The end came on the count of the seventeenth permutation –no need to continue sorting.  It’s kinda dumb to continue looking for something after you have found it, isn’t it?

That is all Miss "brainpower". By the way, who made the spokesperson for Mr. heureka?

That’s Herr Heureka, and I’m not his spokesperson (though I’m sure he wouldn’t mind).  One of my principal jobs is to break up the massive, hardened piles of BS that dam and plug the antiquated sewage system on this forum. We genetically enhanced Chimps prefer to navigate in sewage-free environments.

It is amazing how some of the littlest pip-squeaks will produce some of the largest piles –probably because they are full of it. This is usually a thankless job, but someone needs to do it.  This makes the environment much more healthy and efficient.

GA

GingerAle  Jul 10, 2018
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Aren't you that Irish "Si.....ck Mick", who suffers from OCD, severe anxiety disorder, delusional paranoia...etc.....etc. Do you think anybody on this forum takes you seriously, you self-appointed "cleanser?". You obviously know nothing about programming a computer! For a simple computer program, written correctly, it takes one-thousandth of a second to print 24 permutations, you self-admitted "ape"!

Jul 10, 2018
#8
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Aren't you that Irish "Si.....ck Mick", who suffers from OCD, severe anxiety disorder, delusional paranoia...etc.....etc.

You are a charmer, Mr. Pip-squeak.

Let’s see: The only major OCD I have is avoiding infection from those who have CDD (Contagious Dumbness Disease), BSSS (BatShit Stupidity Syndrome), and other quantum level stupidities that relay Spooky Dumbness at a distance indeterminate, and through any medium.

Yes, delusional paranoia has manifested in the past few weeks. This is because summer break has freed time for the younger dumb-dumbs to visit the forum and spread their CDD.  When the quantum dumbness reaches a certain point, the dumb-dumbs appear to me as gnome-banshee hybrids.

This is a non-bizarre delusion though, because I know the gnome-banshee hybrids are my creation. I use them as an anthropomorphic metaphor to represent the extremes of common human behavior. Interestingly though, when I refer to them in context, most seem to understand the metaphor without needing an explanation. You need an explanation, which is partly why I’m writing this.

Do you think anybody on this forum takes you seriously, you self-appointed "cleanser?".

Yes, I do think the readers of my posts “take” me seriously. To clarify, I think most of the (adult) members who read my posts, correctly interpret my position in context.   I doubt that you do.

The math posts are easy to quantify, the math is either correct or not, sometimes there is an issue on the interpretation of the question –especially for questions relating to combinatorics.  This often is the case in the academic environment too.

My troll posts are a mixed bag.  They put off some people, while others find them hilarious.  Again, I’m sure most understand the hyperbole and metaphors I use to make a point.

While “taking me seriously” is a subjective measure, there is one measure that is not subjective. That is the view counts.

Many read my postings. After I make this post, the view count will climb by at least 12 views in twenty-four hours. These are unique; it does not count the previous readers who read the new post. There will be at least 40 views on this post by this time tomorrow.  By comparison, there have been two unique views since you made your latest post. However, several of the previous readers may have read your post.

If I post a solution to a view count mathematics question with high interest potential, or make a major troll post, then that post’s view count will climb by 15 to 25 in a day, and my previous 40 historical posts view counts will climb by a ten points each and by about 6 points each for the earlier ones.  This seems serious.

You obviously know nothing about programming a computer!

Humm... how is it obvious?

For a simple computer program, written correctly, it takes one-thousandth of a second to print 24 permutations,

That seems very slow for a modern computer or even an antiquated computer.  I suppose there is a proper balance:  a slow computer for a slow brain.   I’m curious; does your computer know anything about human programming?  Anyway, it doesn’t really matter how fast the computer is, if the coded instruction directs it to stop sorting, then it stops sorting. You should know that, if you know anything about programming.

I’m very proud of my ape heritage.  There are about 270,000 chimps in the world and only 16 have genetic enhancement.  I’m one of them.

I’m very proud of my “Mick” heritage too.

I’m not really a “Mick” though; I’m an O’ ... Ginger Alexandra O’........

Though I hope not, I’m sure I’ll be reading more of your nit-picking blarney, and brain-dead analysis.  Until then, I’ll be enjoying a few fermented bananas, while my computer analyzes the next steeplechase.

GA

Jul 10, 2018
#10
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Look at the CORRECTION heureka made this morning, you lunatic idiot!!

Guest Jul 10, 2018
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Heureka didn’t make a correction because nothing is incorrect about the list. The question asks for the 17th alphabetical permutation –that’s all that’s needed for a correct answer. Heureka alphabetized the list because it bugs you; he’s a nice person. I’m not; I would have deranged all of them except for #17, just to make a point.

A curious question: When you eat alphabet soup, do you alphabetize the spoonful of letters before you eat it?

You might like one of these more.

Words alphabetized:

ehnW ouy aet aabehlpt opus, do ouy iaabeehlptz eht flnoopsu of eelrstt beefor ouy aet it?

Word order alphabetized:

alphabet alphabetize before do eat eat it? letters of soup, spoonful the When you you you

Both words and word order alphabetized:

aabehlpt aet aet beefor do eelrstt ehnW eht flnoopsu iaabeehlptz it? of opus, ouy ouy ouy

You now might have some interesting dictionary dreams. BTW, a dictionary is a book used in the old days to look up the spelling and meaning of words.

GA

GingerAle  Jul 10, 2018
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Ginger, I’ve often thought it would be the excess of booze and cigars that would finish me off. They’ve already pushed me into the borrowed time zone.  I never thought it would be from reading posts on a math forum.  I’m close to laughing myself to death.

Dying from laughing seems like a good way to go. I can think of only one other way that might be better.

Jul 11, 2018
edited by Guest  Jul 11, 2018
#15
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Laughter is usually among the best of medicines; although, I suppose it could top-off someone on the edge.  Anyway, you’ve had a few maga-doses and it’s not topped you yet, so keep borrowing from the borrowed-time zone –the interest rates are cheap, and though the days are getting shorter, you’ll have more of them, and you’ll make it up in volume.

What’s the “other way” that might be better?

GA

GingerAle  Jul 15, 2018