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?
Just picture all the 2's and 4's with extra dots turning them all into 6's, say.
To all intents and purposes they're the same, same as the 1's, 3's and 5's.
Twos, fours, and sixes, Oh MY! This sounds like analysis using magical incantations and charms. “Snake eyes and boil, slick lies and toil, these ducks are now pigs.” The ducks aren’t really pigs, but some members of the viewing audience may think they are. This is entertaining, but not as much as using telekinetic powers to roll snake eyes or not snake eyes.
DC Thomas, my cat, demonstrated his telekinetic powers for rolling snake eyes. This was very impressive to watch. He rolled snake eyes on about 60% of the attempts. The dice seemed to roll with normal expectation when he wasn’t using his telekinetic powers. This went on for a while, until Mr. Peabody, my dog, caught him switching out the loaded dice. The fight was on...
DC knows he’ll get caught when he uses loaded dice playing craps, or embezzles Monopoly money when he’s the banker. He does this just to pissoff Mr. Peabody –he likes to fight. Mr. Peabody always obliges. Long ago, I started securing the fragile artwork, and put the veterinarian on speed-dial, whenever we play games.
The (4!) is in there for the same reason it’s in your solution. Four of the dice are indistinguishable from each other, so their permutations are factored out of the (10!).
To clarify, though the four dice appear to be distinguishable from each other because 2, 4, and 6 are distinguishable, they are treated as an indistinguishable group, that is, they are only distinguishable from the 1, 3, and 5. So this question has four groups: three groups of 2 indistinguishable element, each consisting of 1s, 3s, and 5s, and one group four that is an indistinguishable collective of NOT 1s, 3s, or 5s.
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.
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.
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.
So, to answer your question, yes, readers of my posts “take” me seriously enough to read my posts. .
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.
you self-admitted "ape"!
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.
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.
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.
If someone asked me to turn my back while they rolled two dice onto a table top, and then asked me how many 1's I would expect to see when I turned round to look at them, I would say that I expected to see none.
Really? That’s blòódy amazing! So then, if you watched the dice roll then you would expect to see ones every time. You must have telekinetic powers.
Perhaps, when you are not watching, you are unable to control your telekinetic powers to produce a one (1), and in fact cause the dice to roll to every number except a one. That is still impressive!
Of course, you might just have very low expectations. Are you pessimistic by nature?
If you are not using telekinetic powers and this still happens then maybe you’ve entered the quantum realm, where the very act of measuring something changes the result. This relates to the Heisenberg Uncertainty Principle. (I’d explain this, but I’m not sure how to dumb-it-down to your education and intelligence level.)
However, if you resist using your telekinetic powers, and leave the dice to roll naturally –without influence, then the mathematical expectation for rolling two dice and having at least one (1) “single pip” show on one die is (1/3). (Note: in case you didn’t know, a “single pip” means a “one” on a die.)
Anyway, this question is about mathematical expectation, not your personal expectations.
What you posted is a Binomial CDF. This is the Cumulative Distribution Function for a binomial probability, not mathematical expectation. The mathematical expectation does not change –no matter how many times you do this experiment. If it did change, then the Binomial CDF would also change.
It’s great to have (another) “erudite” idiot to troll! We genetically enhanced chimps truly enjoy trolling “erudite” idiots. If you stay around long enough, I’ll give you a name.
The expectation is 92%, that you will continue posting for at least six weeks. What’s the Binomial CDF for this?
My dog, Mr. Peabody, and cat, DC Copper, have reviewed my post, now they want to shoot craps. DC says he wants to test his telekinetic powers for rolling snake eyes. This should be entertaining!
I calculated “the expected number of 1's obtained” on a single roll of two dice.
If this were a roll of one die, then the expectation would be (1/6). However there are two dice, so the expectation is weighted by a factor of two (2), giving 2*(1/6)=(1/3).
Though mathematical expectation and probability are closely related, they are not the same thing. One notable difference is a probability is always a value between zero (0) and one (1), and an expectation may be equal to any (real) number. This value depends on the quantity of interest and on the measured probability. Some probabilities do not have a mathematical expectation, but all mathematical expectations have at least one associated probability.
My troll post, below, contrasts the mathematical expectation to that of a Binomial CDF.