GingerAle

For sure, Presh Talwalkar is a skilled mathematician and articulate teacher of the subject, but the arbitrary pile of BS in the introduction means he was asleep at the calculator when he made this video.

The first thing that came to mind while watching the video is why is the square root allowed? If the cube root is not allowed because it introduces a three (3) the square root should not be allowed because it introduces a two (2).  “...You cannot introduce any new digits, so the cube root is not allowed because it involves the digit (3).”  (In any case, the last time I checked, the cube root function is not a digit, so the reason is a complete non sequitur.)

I noted a comment posted thirty months after the introduction of the video making this point.  The 479 responses both agree and disagree that the square root introduces a (2). 

I might assume the arbitrary allowance for square roots in solving four of these problems comes from Brazilian math theory, which isn’t always consistent. Dragonlance hilariously points this out:

If I choose four cards from a standard 52-card deck,with replacement, what is the probability that I will end up with all four Aces?

This question is poorly written. The primary defect is the phrase “end up with all four Aces,” which is a colloquialism as used here. The capital “A” in “Aces” is nonstandard, and gives ambiguous emphases to the word aces. Use of the word “all” could imply different suits for the four aces, rather than some combination of aces where one or more is repeated.  

This is a primer statistics question so a reasonable interpretation is:

If I choose four cards from a standard 52-card deck, with replacement, what is the probability that I will select four aces of different suits?

The phrase “with replacement” is an explicit standard variation in the sampling method. In this case, it means the card (no matter what it is) is replaced after it is drawn.  It’s also important to note that the deck or selection process remains randomized after the card is replaced.

A success in this experiment is four aces in four different suits.  Any other combination is a failure.

\(\dfrac{4}{52}*\dfrac{3}{52}*\dfrac{2}{52}*\dfrac{1}{52} =\dfrac{3}{913952} \)

This happens about (3) times per million attempts. It’s noteworthy that EP’s solution is correct and (mostly) matches this, which also happens about (3) times per million attempts. 

IF...

A success in this experiment is four aces without regard to the suit. 

\(\left(\dfrac{4}{52}\right)^4   =  \dfrac{1}{28561}\)

This happens about (35) times per million attempts.

GA

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Guest’s answer is wrong. So it appears he didn’t learn it.

There are numerous examples of online poker-hand probability texts and examples. Google is a good starting point ...Bing is too.... so is Yahoo.... and Dogpile....

Solution for this question:

Choose the rank for the triple nCr(13,1)

Choose three suits for the triple nCr(4,3)

Choose a different rank for the pair nCr(12,1)

Choose two suits for the pair nCr(4,2)

Then

Divide this by the total number of five-card hands. nCr(52,5)

\(\hspace {7cm} \large \text{ } \dfrac{\dbinom {13}{1}\dbinom {4}{3}\dbinom {12}{1}\dbinom {4}{2}}{\dbinom {52}{5}} = \dfrac{6}{4165} \approx 0.144\% \)

GA

An internet search might well produce a closed form expression for the n'th term.

You’re right; there is one:

\(L_n = \dfrac{1-sqrt(5)}{2}^n + \; \dfrac{1+sqrt(5)}{2}^n \)

The sequence starts with n=0, so the 100^th term is n=99

n=99;((1+sqrt(5))/2)^n+((1-sqrt(5))/2)^n

The web2.0calc has a rounding error greater than -2.6

Wolfram gives (489526700523968661124). Dividing this by (20) gives a remainder of (4).

GA

Morgan Tud’s Magick of the Quadratic gives an animated formulaic and pictographic overview of the process. 

Hi Ron,

I definitely recognize your style. I have several lists with guests post links; though none have as many links as your file. The next closest are the BB (1-4) files, which I quit saving the links to years ago.  Most guest posters do not post for long, or they becomes members

I noticed your white dot early on. This made it very easy to confirm your posts, but about 3.5% of the posts I have in your list do not have this dot. So, either I’m wrongly attributing them to you, or you do not use the dot all time.  Also there are occasional posts on here that have a dot but do not seem like they belong to you.   

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Demands on my time have reduced my posting; although in the past few weeks I have made a few posts as a guest; I’ll collect my copyrights at some point, except for the posts I don’t want cluttering up my profile. 

Here are three threads:

This question is not nonsense; it's just wrongly typed.  

Jugoslav corrected the question and gave the right answer! 

Let’s see...

Eeny, meeny, miny, moe,

*Wrongly typed question ... has no solutions as presented. 

*Wrongly typed question could equal nonsense.

*Correctly typed question presented by a teacher to demonstrate that some questions have no solution. 

Catch a solution by the toe....

*Modify wrongly typed question by transposing angles A and B.  Solve

*Modify correctly typed question presented by a teacher to demonstrate that some questions have no solution, by transposing angles A and B and solve, defeating the purpose of the teacher presenting a question that has no solution. 

Eeny, meeny, miny, moe,

Me mum says to pick the very best one ... but which one is it? 

GA

Ok.... Here are some convincing reasons for my use of the adjective “atrocious,” and for your nomination for the Fields MeTal: “Mind Numbingly Atrocious” category. (You can see this identifying category by mousing over the emoji at the end of my first post,)

The question you attempted to answer is an introductory level geometry question. A moderately practiced student should be able to answer this question in about 5 to 7 minutes.  After composing the equations, solving, and checking, I then examined your solution.

At first glance your solution looked like a rambling string of hodgepodge equations. I’d never seen anything like this before. I thought perhaps you may have taken a unique, less traveled, solution path to contrast the sometimes hidden mathematical relationships that come to light while solving a problem. I also thought the six points on your post, which is a lot –even for a masterpiece solution, was for your wonderful unique solution.   

With a closer inspection, I examined the path and followed the circuitous route, which lead into left field, through cactus, bramble bushes, and a cesspool –the route was brutal, and then at the end where the result should be was a gaping hole. The hole wasn’t because you didn’t post the numeric answer, it’s because you wrote B=MCB, and MCB is not defined in your solution path.   I don’t know what was in that hole, but it wasn’t an answer. 

I spent 45 minutes analyzing your equations. Ten minutes into the process, my brain started overheating and going numb. I ignored the warning alarms and continued. At 45 minutes the thermal circuit breakers tripped and the higher functioning parts of me brain shut down. 

While I was unconscious, I dreamt I went to heII. Itwas a pretty good dream: while I was down there, I saw Sister Alice –she was my math teacher for 7^th, 8^th, and the first half of 9^th grades.  Little devils were stabbing her with pitchforks inscribed with errant math equations –including one with your equation. I woke up to my cat laying on me, licking my face. I don’t think he was concerned about me; he just wanted some fermented tuna juice.

After giving my cat his fermented tuna juice, I returned to your solution. I noticed your equations had a similar aroma to the fermented tuna juice.

I decided to nominate your solution for the Fields MeTal Prize. For obvious reasons, I chose the “Mind-numbingly Atrocious” category.  If there was a Smells Like Fermented Fish Category, or Sour Orange Juice category I would have nominated it for those too. 

I doubt you will win, but you should get an honorable mention.

I sent a proposal to the Fields MeTal Board of Directors, suggesting a new category: Equations Worthy of Inscription on Pitchforks Used in HeII.

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One more thing: you shouldn’t inflate the points on your posts. Doing that devalues the legitimate points given to you by others. 

GA