Clippy was discontinued long enough ago that this may require the geezers category!

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I feel like the Westminster Balloon Kennel Club would be better prepared than to buy pins for the winner ribbons.

Having been involved with FIRST LEGO League (the grade-school precursor to high-school FIRST Robotics) for 20 years, the last one isn’t actually far off. And is therefore either not funny or meta-hilarious (count me in Camp #2).

Nancy’s history with the robotics club (in the Olivia Jaimes era only) has been going on a long time and has had many ups and downs. And always with a tension about members of the same team needing to cooperate for tournaments against rivals, yet experiencing the greatest feelings of competition against members within their own team.

Mitch4: That’s interesting. I know FRC is different from FLL (starting with the kids being older and thus more formed people). I would say I hadn’t noticed this in FLL. One of the really neat things about FLL that the kids don’t seem to ever notice at a conscious level is that their real competition is against their own robot, not the other teams, and not against their teammates.

OTOH I coached an all-girl, all GT team for four years and have been a judge advisor since, so I’m perhaps seeing a very narrow slice of the FLL universe.

PSA: These competitions teach everything you want your kid to learn: science, technology, research, teamwork, and competition, somehow without the focus on the last item that almost everything else seems to have. In 20 years of FLL I’ve seen ONE kid crying at a competition, and there was clearly some other issue there based on how the parent was speaking to him. Compare that to any other kids’ tournament, where someone is always sad. Volunteer for a tournament–they can always use judges and referees! It’s pure fun.

all GT team

I don’t know what that is, and searching didn’t come up with anything that seemed definitive.

My two favorite chicken/road jokes:

Why did the punk rocker cross the road? He was stapled to a chicken.

Why did the chicken cross the road? Because it was too far to walk around.

Brian in STL: Sorry. GT = Gifted & Talented. Like, smart kids. GT girls are VERY different from non-GT boys, especially at that age–if I heard boys’ team coaches talking about intrateam competition I’d have to believe it.

Ah. Sounds fun.

@ Phil Smith III I once attended an interesting talk given by the head of Special Educational Needs in a (UK) county education authority. SEN is usually considered to mean catering for less able kids, but it also means provision for ‘GT’ ones. He was telling us how hard it can be, sometimes, to identify such children early enough by straightforward testing, and he gave an example of how important good teaching and good teacher insights were in the early years of school.

He didn’t say how old the children were, but we can guess a likely age range when they’d have a question like this in a class quiz:

Out of these, which is the odd one out?

TENT
CAVE
TRACTOR
HOUSE

One boy, who the teacher knew was very bright, gave the “wrong” answer. Rather than just mark him down, the teacher asked him why he had picked the one he did.

I’ll return later with what the “right” answer was, what the boy picked, and why.

I’ll guess he chose “cave:” the others are manufactured or human-built.

Yea, that’s the trouble with these kinds of questions and the idea that there are ‘right’ answers to them. There are a variety of possible answers if you think about it. Could be ‘tent’ as it’s the only one that starts and ends with the same letter. Could be ‘tent’ because it’s the only word with just one vowel. Could be ‘house’ as it’s the only one that doesn’t start with a hard consonant. And on and on and on…

There was a little furore a couple of years ago where Clippy was introduced to Microsoft Teams, then rapidly unintroduced a day later. I don’t think much else happened in 2019, so it may be a little memorable.

@ Stan – the thing to remember is that this question was asked of (we guessed) 7-8-year olds, surely no older than 9.

The “right” answer was tractor, as you can live in all of the others. But as per Lost in A**2, cave is valid as it isn’t man-made. (Well, it can be, but that level of analysis is probably not expected at this level of education).

He picked house.

What scared us (all parents of gifted children) was the reasoning of this 8±1 year old when asked why.

He’d seen cave, the only natural one, and tractor, the only non-shelter one, reasoned that as 2 possible answers made the question faulty, it couldn’t have been about the objects themselves, it had to be about the words and picked house as it’s the only one you can’t put ‘CON’ in front of to make another word.

“@ Stan – the thing to remember is that this question was asked of (we guessed) 7-8-year olds, surely no older than 9.”

Are you saying this age group can’t recognise letters, as in ‘tent’ starts and ends with the same one? Or doesn’t know the difference between vowels and consonants? I’m not sure what point you’re trying to make. There are probably dozens of ways 7 – 9 year olds could find differences between these words.

However, that ‘con’ one was pretty good, I must say. Move that kid to the top of the class!

@Shrug — first new chicken joke I’ve heard in years:
Why did the chicken cross the road?
(I dunno)
To MURDER you. Knock Knock.
(Who’s there?)
THE CHICKEN!

I thought it was “tractor” because that was the only word that did not contain an “E”.

These are all great. The test should have had an ‘explain your reasoning” to be useful, eh?

This is why I hated the SATs, though I did fine on them. “Try not to think about it…”

I appreciate your point Mike P, that it wasn’t merely that the kid picked a different answer, but the double bluff that he reasoned it must be the answer sought because there were two such obvious candidates for the “right” answer, that neither of them could be the right answer.
Sadly, though, I would see this as evidence that he had been exposed to too many of these stupid standardized tests before, that you’re always looking for the trick, and then the problem is evaluating (guessing) how smart the test writers are and answering appropriately to their level of perceived intelligence.

The problem is glibly admitted: you have 30 minutes to answer 60 questions (or whatever), which means that you have only 30 seconds per question. So especially in math, none of the questions can be real world problems, and they are not just simple identification questions. So by definition they are going to be “trick” questions, where once you realize the trick, you can instantly definitively solve them and know you have the right answer, something that rarely occurs in the real world. If I’m told a bunch of things about a bridge, say, I’m going to have to plug in numbers and laboriously do messy calculations with only approximate answers to best answer what it is I need to know, and it’s going to be time consuming proportionate to the better I want my answer to be — it’s not going to be doable in 30 seconds, and any answer I might come up with in 30 seconds is just going to be a very, very rough approximation, possibly giving me the direction and magnitude of the answer, but no more. Though valuable in the real world (like for checking that the supposed correct answer even makes sense), that is never the information these 30 second trick questions want — they want a complete, perfect answer. So usually this means that there is a multiplication by 0 or some such a few steps in, so that as soon as you spot it, you can say, ah, zero, next question.
So these are never fair questions testing your actual real world knowledge and skills, they are always trick questions testing your test-taking abilities, and the hard part is figuring out how smart the test makers were to figure out how deep and deceptive the tricks are — you see that there’s a term that multiplies everything by zero, can you stop and say zero and move on, or do you have to keep searching to see if they then raise everything to the power of that term that gets multiplied by zero, making the answer one? And then there’s the linguistic crap they pull, especially in the supposed math sections, where they say something like “find the best answer”, vs “find an answer” — in the first case, if you didn’t clue in, you might be tempted to give the first correct answer you find, which would be wrong (how perverse is that?), whereas in the second case, you might waste time fretting that none of the answers are completely correct (by which I mean “complete”, not that they are somewhat wrong — they are not that “best” possible answer, but they are technically correct), until you realize that in this case you don’t need the best answer, so the crappy but technically correct answer in this instance is what they want…
Add to this that if you are ADHD, you can get an exemption from the time restriction of these test, which of course totally changes the ball game, so the tests are not even “standardized” anymore, you are comparing apples and oranges… If I could have gotten a time exemption when I took the SATs, I’m pretty sure I could have gotten close to perfect scores, which possibly could have changed the course of my life (probably not really in my case, I did well enough, and got into a good enough school, but still…). And it turns out I probably do have ADHD I recently discovered…
Bleargh! A pox on all their houses…

Very interesting discussion of testing, and this particular question. The twist or trick as I saw it, apart from the double-bluff meta aspect of the story with this one kid, was about whether the “which one doesn’t fit” question can be about the form of the words or must always be about the referents of the words. I thought in reality these are about the things named — yet so many of our “creative” alternate answers were about the words. — As was the youngster’s in the story. Isn’t that as much a sign of his lateral creativity as the appeal to the psychology of test construction?

Mitch4: Yes. My comment on this to my sisters was that this kid is headed either for greatness or crushing disappointment.

“TRACTOR” is distinguished from the others in at least 3 ways, so gets my vote. a) it is the sole entry in which one doesn’t live; b) it is the sole entry not containing an “E”; and c) it is the sole entry having more than one syllable.

“TRACTOR” is also d) the sole entry having an “R”.

(He) picked house as it’s the only one you can’t put ‘CON’ in front of to make another word

The Marilyn Vos Savant column in Parade frequently has word puzzles along those lines. I’m not sure if a kid would be likely to read that.

Brian in STL: What present-day kid has ever seen a Sunday newspaper?

I found a way to quickly answer the “what’s the next number in the series” questions: find the difference in each pair of numbers.

What’s the next in 1, 3, 5, 7, 9? 3-1 = 2, 2, 2, 2, so it’s 11.

What’s the next in 1, 4, 9, 16, 25? 3, 5, 7, 9, do it again, 2, 2, 2, 2, so 9 + 2 is 11, so 36.

What’s the next in 31, 28, 31, 30, 31? First: -3, 3, -1, 1. Then: 6, -4, 2. Then: -10, 6. Then 16. Add 16 to get -10, 6, 22. Then 6, -4, 2, 24. Then -3, 3, -1, 1, 25. Finally you know the last difference so the series is 31, 28, 31, 30, 31, 56.

I got about 80% correct on the test.

MiB, and the one with the constant second-order differences happens to also be the series of the squares.
I write “happens to” but of course it isn’t just a happy accident.
At what grade level would you expect students to prove that? (Or to go back a step, at what level would you expect a teacher to be able to formulate it as a statement their students could understand and try to prove.)
(And there is an area called the calculus of finite differences.)

larK –

I never finished getting a CPA which did not matter in terms of being allowed to prepare income tax returns at the time. IRS then decided that non-CPAs (and non- lawyers, or those in a few categories) had to take a exam to be allowed to prepare income taxes – unfortunately there are several versions of my name that I use with varying of married, maiden -either/or/combined and versions of first name as when I use both last names I end up using my first initial only, etc. I ran into a problem – I did not have ID which exactly matched the name that IRS had for me as preparer and therefore could not take the exam. While I was trying to resolve this problem IRS switched to an annual education requirement for those who not yet passed the exam. So every year I have to take 20 hours of classes. I take the classes online (from a private company) and have to pass the exams for the classes to get credit.

There is a specific 6 hour class (with 3 hour exam) that must be taken, but the rest of the classes can be selected from a list of classes that the company offers. At this point in time I have only 5 clients (and one of them died recently and another is not required to file a return, but gets a refund from NYC if she files a NYS?NYC return against taxes paid and does not file a Federal return ) and their returns are rather straightforward – nothing exciting. When dealing with interest, dividends, and 1099-Rs what is contained in the classes and the exams basically does not apply to any of them (or our own return). I would pick classes that sounded interesting – such as “the Gig Economy”, as well as basic tax info. The it dawned on me – since the information is not really of use to me why I am wasting time reading all of this – I can always look it up if it is actually needed. I now download the courses I am going to take and put them on my laptop on my desk. I open them one at time and take the exam on my desktop computer. If I do not know the answer I turn to my laptop and search the course text for the correct answer – I generally get a high 80s score on each of the exams.

Mitch4: Yes, my method turns out to work for just about any polynomial series. But if it’s a 10th-order polynomial there will have to be a lot of terms to start you off.

I didn’t know anything about calculus at the time, but eventually I learned about Babbage’s Difference Engine. He never constructed one in his lifetime, but later someone named Scheutz did. Differences are calculus with d instead of delta. The ENIAC computer could and often did function as a difference engine, but it could do other kinds of computations as well.

MiB, the next number in the series is 30. As long as it’s not a leap year.

@ Brian in StL – I quit reading Ms. Savant’s column after she first published an incorrect answer to a probability paradox, and then, after after the error had been identified and corrected in a reader’s letter, she doubled down, insisting that her incorrect solution was the right one. She may have a brilliant facility for answering IQ test questions, but she also has a talent for thickheadedness.

Which one?

I was wondering also — could it be the Monty Hall puzzle? But I thought she was seen to be correct on that one. Maybe it was “A woman has two children. One is a boy. What is the probability the other one is a boy?”.

Treesong: Brilliant!

According to Wikipedia, Savant tackled both the Monty Hall problem, and the two boys problem, both to similar outrage, the first in 1990, and the second in 91-92, and again in 96-97. In both cases she ultimately had to resort to empirical evidence, actually having the trials run hundreds of times, to convince recalcitrant readers that regardless of what they think the obvious logic is, when one actually runs the trials in the real world, the odds come out as she had insisted they would. For Monty Hall, she had school teachers run the setup with their students, and in the end had more than 1000 trials which showed you should always switch; for the two boys problem, she asked female readers with exactly two children, at least one of them male, to give the sex of both children, and got nearly 18,000 responses, which showed that 1 in 3 had two boys…

(Wikipedia mentions two errors she had to retract, one in 2012, one in 2014, but I think Kilby had long since stopped reader her by then…)

I took issue with one of vos Savant’s probability puzzles. A dog has four puppies. What is the most likely combination of males and females? I say two males and two females, 6 out of 16. She said one male and three females or one female and three males, 8 out of 16.

I wrote her a letter:
Dear Ms. vos Savant, I was arguing with my friends about the most likely outcome of throwing a pair of dice.

Bill said the most likely outcome is a 7, with a chance of 6 out of 36.
Ted said no, you are more likely to get an even number, with a chance of 18 out of 36.
I say the most likely outcome is a number between two and twelve inclusive, with a chance of 36 out of 36.

Who is correct?

She never replied.

She said one male and three females or one female and three males, 8 out of 16.

Well, when phrased that way, with the or and the clearly described cases, the phoniness is easy to spot. But it might fool some people some of the time if phrased “three of one sex and one of the other.”

I did my own empirical test of Monty Hall problem. It’s a pretty easy program to write and you can do as many trials as you like. I had a hard time wrapping my head around the logic solutions, but the empirical results showed me that it was correct. As I recall, Mythbusters tested it with a bunch of volunteers.

“Three of one sex and one of the other” is probably what vos Savant meant, but not what she wrote.

All four same sex: 2 out of 16.
Two of each: 6 out of 16.
Three and one: 8 out of 16.

But there’s a big difference between getting three males and a female and three females and a male when it’s time to give away or sell the pups. Almost everyone seems to want a male.

@ Brian in STL – in this country, even were it still being published, no kid would be likely to read Parade (one hopes).

NSFW: any google/bing/etc image searches for the magazine.

Mike P: Ah yes, as a callow “ute” 45+ years ago, I remember fondly a few magazines like that Parade. You confused me for a sec because I missed the “British” and was thinking “We get what’s left of Parade every Sunday…it’s boring and silly but hardly NSFW!” Wrong parade. Send in the clones.

One advantage (among many) to no longer being a productive member of society is that NSFW is not a concern.

If I were a kid and my parents were getting the Sunday paper, I would probably still read Parade. The number of households getting the physical newspaper is much reduced these days.

Unless the ‘W’ stands for ‘wife’ 😉

MiB sez: Mitch4: Yes, my method turns out to work for just about any polynomial series. But if it’s a 10th-order polynomial there will have to be a lot of terms to start you off.

I recall seeing something like that worked out, in a humorous-but-valid book called “Mathematics made Difficult”. (I also recall later looking for the book and seeing it out of print but for sale by Amazon resellers for a small fortune.)

There’s one on eBay (US) right now for about $100.

And there’s a “Mathematics Made Difficult” at the Braintree Public Library – much cheaper than ABE. I just put it on hold. Thanks for the reference, Mitch4.

I feel like the Westminster Balloon Kennel Club would be better prepared than to buy pins for the winner ribbons.

Having been involved with FIRST LEGO League (the grade-school precursor to high-school FIRST Robotics) for 20 years, the last one isn’t actually far off. And is therefore either not funny or meta-hilarious (count me in Camp #2).

Nancy’s history with the robotics club (in the Olivia Jaimes era only) has been going on a long time and has had many ups and downs. And always with a tension about members of the same team needing to cooperate for tournaments against rivals, yet experiencing the greatest feelings of competition against members within their own team.

Mitch4: That’s interesting. I know FRC is different from FLL (starting with the kids being older and thus more formed people). I would say I hadn’t noticed this in FLL. One of the really neat things about FLL that the kids don’t seem to ever notice at a conscious level is that their real competition is against their own robot, not the other teams, and not against their teammates.

OTOH I coached an all-girl, all GT team for four years and have been a judge advisor since, so I’m perhaps seeing a very narrow slice of the FLL universe.

For anyone wondering what we’re on about here, check out https://www.firstlegoleague.org/ and https://info.firstinspires.org/

PSA: These competitions teach everything you want your kid to learn: science, technology, research, teamwork, and competition, somehow without the focus on the last item that almost everything else seems to have. In 20 years of FLL I’ve seen ONE kid crying at a competition, and there was clearly some other issue there based on how the parent was speaking to him. Compare that to any other kids’ tournament, where someone is always sad. Volunteer for a tournament–they can always use judges and referees! It’s pure fun.

all GT teamI don’t know what that is, and searching didn’t come up with anything that seemed definitive.

My two favorite chicken/road jokes:

Why did the punk rocker cross the road? He was stapled to a chicken.

Why did the chicken cross the road? Because it was too far to walk around.

Brian in STL: Sorry. GT = Gifted & Talented. Like, smart kids. GT girls are VERY different from non-GT boys, especially at that age–if I heard boys’ team coaches talking about intrateam competition I’d have to believe it.

Ah. Sounds fun.

@ Phil Smith III I once attended an interesting talk given by the head of Special Educational Needs in a (UK) county education authority. SEN is usually considered to mean catering for less able kids, but it also means provision for ‘GT’ ones. He was telling us how hard it can be, sometimes, to identify such children early enough by straightforward testing, and he gave an example of how important good teaching and good teacher insights were in the early years of school.

He didn’t say how old the children were, but we can guess a likely age range when they’d have a question like this in a class quiz:

Out of these, which is the odd one out?

TENT

CAVE

TRACTOR

HOUSE

One boy, who the teacher knew was very bright, gave the “wrong” answer. Rather than just mark him down, the teacher asked him why he had picked the one he did.

I’ll return later with what the “right” answer was, what the boy picked, and why.

I’ll guess he chose “cave:” the others are manufactured or human-built.

Yea, that’s the trouble with these kinds of questions and the idea that there are ‘right’ answers to them. There are a variety of possible answers if you think about it. Could be ‘tent’ as it’s the only one that starts and ends with the same letter. Could be ‘tent’ because it’s the only word with just one vowel. Could be ‘house’ as it’s the only one that doesn’t start with a hard consonant. And on and on and on…

There was a little furore a couple of years ago where Clippy was introduced to Microsoft Teams, then rapidly unintroduced a day later. I don’t think much else happened in 2019, so it may be a little memorable.

@ Stan – the thing to remember is that this question was asked of (we guessed) 7-8-year olds, surely no older than 9.

The “right” answer was tractor, as you can live in all of the others. But as per Lost in A**2, cave is valid as it isn’t man-made. (Well, it can be, but that level of analysis is probably not expected at this level of education).

He picked house.

What scared us (all parents of gifted children) was the reasoning of this 8±1 year old when asked why.

He’d seen cave, the only natural one, and tractor, the only non-shelter one, reasoned that as 2 possible answers made the question faulty, it couldn’t have been about the objects themselves, it had to be about the words and picked house as it’s the only one you can’t put ‘CON’ in front of to make another word.

“@ Stan – the thing to remember is that this question was asked of (we guessed) 7-8-year olds, surely no older than 9.”

Are you saying this age group can’t recognise letters, as in ‘tent’ starts and ends with the same one? Or doesn’t know the difference between vowels and consonants? I’m not sure what point you’re trying to make. There are probably dozens of ways 7 – 9 year olds could find differences between these words.

However, that ‘con’ one was pretty good, I must say. Move that kid to the top of the class!

@Shrug — first new chicken joke I’ve heard in years:

Why did the chicken cross the road?

(I dunno)

To MURDER you. Knock Knock.

(Who’s there?)

THE CHICKEN!

I thought it was “tractor” because that was the only word that did not contain an “E”.

These are all great. The test should have had an ‘explain your reasoning” to be useful, eh?

This is why I hated the SATs, though I did fine on them. “Try not to think about it…”

I appreciate your point Mike P, that it wasn’t merely that the kid picked a different answer, but the double bluff that he reasoned it

mustbe the answer sought because there were two such obvious candidates for the “right” answer, that neither of themcouldbe the right answer.Sadly, though, I would see this as evidence that he had been exposed to too many of these stupid standardized tests before, that you’re always looking for the trick, and then the problem is evaluating (guessing) how smart the test writers are and answering appropriately to their level of perceived intelligence.

The problem is glibly admitted: you have 30 minutes to answer 60 questions (or whatever), which means that you have only 30 seconds per question. So especially in math, none of the questions can be real world problems, and they are not just simple identification questions. So by definition they are going to be “trick” questions, where once you realize the trick, you can instantly definitively solve them and know you have the right answer, something that rarely occurs in the real world. If I’m told a bunch of things about a bridge, say, I’m going to have to plug in numbers and laboriously do messy calculations with only approximate answers to best answer what it is I need to know, and it’s going to be time consuming proportionate to the better I want my answer to be — it’s not going to be doable in 30 seconds, and any answer I might come up with in 30 seconds is just going to be a very, very rough approximation, possibly giving me the direction and magnitude of the answer, but no more. Though valuable in the real world (like for checking that the supposed correct answer even makes sense), that is

neverthe information these 30 second trick questions want — they want a complete, perfect answer. So usually this means that there is a multiplication by 0 or some such a few steps in, so that as soon as you spot it, you can say, ah, zero, next question.So these are never fair questions testing your actual real world knowledge and skills, they are

alwaystrick questions testing your test-taking abilities, and the hard part is figuring out how smart the test makers were to figure out how deep and deceptive the tricks are — you see that there’s a term that multiplies everything by zero, can you stop and say zero and move on, or do you have to keep searching to see if they then raise everything to the power of that term that gets multiplied by zero, making the answer one? Andthenthere’s the linguistic crap they pull, especially in the supposed math sections, where they say something like “find thebestanswer”, vs “find an answer” — in the first case, if you didn’t clue in, you might be tempted to give the first correct answer you find, which would be wrong (how perverse is that?), whereas in the second case, you might waste time fretting that none of the answers are completely correct (by which I mean “complete”, not that they are somewhat wrong — they are not that “best” possible answer, but they are technically correct), until you realize that inthiscase you don’t need thebestanswer, so the crappy but technically correct answer in this instanceiswhat they want…Add to this that if you are ADHD, you can get an exemption from the time restriction of these test, which of course

totallychanges the ball game, so the tests are not even “standardized” anymore, you are comparing apples and oranges… If I could have gotten a time exemption when I took the SATs, I’m pretty sure I could have gotten close to perfect scores, which possibly could have changed the course of my life (probably not really in my case, I did well enough, and got into a good enough school, but still…). And it turns out I probablydohave ADHD I recently discovered…Bleargh! A pox on all their houses…

Very interesting discussion of testing, and this particular question. The twist or trick as I saw it, apart from the double-bluff meta aspect of the story with this one kid, was about whether the “which one doesn’t fit” question can be about the form of the words or must always be about the referents of the words. I thought in reality these are about the things named — yet so many of our “creative” alternate answers were about the words. — As was the youngster’s in the story. Isn’t that as much a sign of his lateral creativity as the appeal to the psychology of test construction?

Mitch4: Yes. My comment on this to my sisters was that this kid is headed either for greatness or crushing disappointment.

“TRACTOR” is distinguished from the others in at least 3 ways, so gets my vote. a) it is the sole entry in which one doesn’t live; b) it is the sole entry not containing an “E”; and c) it is the sole entry having more than one syllable.

“TRACTOR” is also d) the sole entry having an “R”.

(He) picked house as it’s the only one you can’t put ‘CON’ in front of to make another wordThe Marilyn Vos Savant column in Parade frequently has word puzzles along those lines. I’m not sure if a kid would be likely to read that.

Brian in STL: What present-day kid has ever seen a Sunday newspaper?

I found a way to quickly answer the “what’s the next number in the series” questions: find the difference in each pair of numbers.

What’s the next in 1, 3, 5, 7, 9? 3-1 = 2, 2, 2, 2, so it’s 11.

What’s the next in 1, 4, 9, 16, 25? 3, 5, 7, 9, do it again, 2, 2, 2, 2, so 9 + 2 is 11, so 36.

What’s the next in 31, 28, 31, 30, 31? First: -3, 3, -1, 1. Then: 6, -4, 2. Then: -10, 6. Then 16. Add 16 to get -10, 6, 22. Then 6, -4, 2, 24. Then -3, 3, -1, 1, 25. Finally you know the last difference so the series is 31, 28, 31, 30, 31, 56.

I got about 80% correct on the test.

MiB, and the one with the constant second-order differences happens to also be the series of the squares.

I write “happens to” but of course it isn’t just a happy accident.

At what grade level would you expect students to prove that? (Or to go back a step, at what level would you expect a teacher to be able to formulate it as a statement their students could understand and try to prove.)

(And there is an area called the calculus of finite differences.)

larK –

I never finished getting a CPA which did not matter in terms of being allowed to prepare income tax returns at the time. IRS then decided that non-CPAs (and non- lawyers, or those in a few categories) had to take a exam to be allowed to prepare income taxes – unfortunately there are several versions of my name that I use with varying of married, maiden -either/or/combined and versions of first name as when I use both last names I end up using my first initial only, etc. I ran into a problem – I did not have ID which exactly matched the name that IRS had for me as preparer and therefore could not take the exam. While I was trying to resolve this problem IRS switched to an annual education requirement for those who not yet passed the exam. So every year I have to take 20 hours of classes. I take the classes online (from a private company) and have to pass the exams for the classes to get credit.

There is a specific 6 hour class (with 3 hour exam) that must be taken, but the rest of the classes can be selected from a list of classes that the company offers. At this point in time I have only 5 clients (and one of them died recently and another is not required to file a return, but gets a refund from NYC if she files a NYS?NYC return against taxes paid and does not file a Federal return ) and their returns are rather straightforward – nothing exciting. When dealing with interest, dividends, and 1099-Rs what is contained in the classes and the exams basically does not apply to any of them (or our own return). I would pick classes that sounded interesting – such as “the Gig Economy”, as well as basic tax info. The it dawned on me – since the information is not really of use to me why I am wasting time reading all of this – I can always look it up if it is actually needed. I now download the courses I am going to take and put them on my laptop on my desk. I open them one at time and take the exam on my desktop computer. If I do not know the answer I turn to my laptop and search the course text for the correct answer – I generally get a high 80s score on each of the exams.

Mitch4: Yes, my method turns out to work for just about any polynomial series. But if it’s a 10th-order polynomial there will have to be a lot of terms to start you off.

I didn’t know anything about calculus at the time, but eventually I learned about Babbage’s Difference Engine. He never constructed one in his lifetime, but later someone named Scheutz did. Differences are calculus with d instead of delta. The ENIAC computer could and often did function as a difference engine, but it could do other kinds of computations as well.

MiB, the next number in the series is 30. As long as it’s not a leap year.

@ Brian in StL – I quit reading Ms. Savant’s column after she first published an incorrect answer to a probability paradox, and then, after after the error had been identified and corrected in a reader’s letter, she doubled down, insisting that her incorrect solution was the right one. She may have a brilliant facility for answering IQ test questions, but she also has a talent for thickheadedness.

Which one?

I was wondering also — could it be the Monty Hall puzzle? But I thought she was seen to be correct on that one. Maybe it was “A woman has two children. One is a boy. What is the probability the other one is a boy?”.

Treesong: Brilliant!

According to Wikipedia, Savant tackled both the Monty Hall problem,

andthe two boys problem, both to similar outrage, the first in 1990, and the second in 91-92, and again in 96-97. In both cases she ultimately had to resort to empirical evidence, actually having the trials run hundreds of times, to convince recalcitrant readers that regardless of what they think the obvious logic is, when one actually runs the trials in the real world, the odds come out as she had insisted they would. For Monty Hall, she had school teachers run the setup with their students, and in the end had more than 1000 trials which showed you should always switch; for the two boys problem, she asked female readers with exactly two children, at least one of them male, to give the sex of both children, and got nearly 18,000 responses, which showed that 1 in 3 had two boys…(Wikipedia mentions two errors she had to retract, one in 2012, one in 2014, but I think Kilby had long since stopped reader her by then…)

I took issue with one of vos Savant’s probability puzzles. A dog has four puppies. What is the most likely combination of males and females? I say two males and two females, 6 out of 16. She said one male and three females or one female and three males, 8 out of 16.

I wrote her a letter:

Dear Ms. vos Savant, I was arguing with my friends about the most likely outcome of throwing a pair of dice.

Bill said the most likely outcome is a 7, with a chance of 6 out of 36.

Ted said no, you are more likely to get an even number, with a chance of 18 out of 36.

I say the most likely outcome is a number between two and twelve inclusive, with a chance of 36 out of 36.

Who is correct?

She never replied.

`She said one male and three females or one female and three males, 8 out of 16.`

Well, when phrased that way, with the

orand the clearly described cases, the phoniness is easy to spot. But it might fool some people some of the time if phrased “three of one sex and one of the other.”I did my own empirical test of Monty Hall problem. It’s a pretty easy program to write and you can do as many trials as you like. I had a hard time wrapping my head around the logic solutions, but the empirical results showed me that it was correct. As I recall, Mythbusters tested it with a bunch of volunteers.

Well, apparently one can load the dice by choosing to breed young males to older females or vice versa, so all bets are off:

https://www.psychologytoday.com/us/blog/canine-corner/201906/the-age-parents-predicts-the-sex-puppies-in-litter

“Three of one sex and one of the other” is probably what vos Savant meant, but not what she wrote.

All four same sex: 2 out of 16.

Two of each: 6 out of 16.

Three and one: 8 out of 16.

But there’s a big difference between getting three males and a female and three females and a male when it’s time to give away or sell the pups. Almost everyone seems to want a male.

@ Brian in STL – in this country, even were it still being published, no kid would be likely to read Parade (one hopes).

SFW: en.wikipedia.org/wiki/Parade_(British_magazine)

NSFW: any google/bing/etc image searches for the magazine.

Mike P: Ah yes, as a callow “ute” 45+ years ago, I remember fondly a few magazines like that Parade. You confused me for a sec because I missed the “British” and was thinking “We get what’s left of Parade every Sunday…it’s boring and silly but hardly NSFW!” Wrong parade. Send in the clones.

One advantage (among many) to no longer being a productive member of society is that NSFW is not a concern.

If I were a kid and my parents were getting the Sunday paper, I would probably still read Parade. The number of households getting the physical newspaper is much reduced these days.

Unless the ‘W’ stands for ‘wife’ 😉

MiB sez:

`Mitch4: Yes, my method turns out to work for just about any polynomial series. But if it’s a 10th-order polynomial there will have to be a lot of terms to start you off.`

I recall seeing something like that worked out, in a humorous-but-valid book called “Mathematics made Difficult”. (I also recall later looking for the book and seeing it out of print but for sale by Amazon resellers for a small fortune.)

There’s one on eBay (US) right now for about $100.

ABE Books has used copies from $77.

https://www.abebooks.com/servlet/SearchResults?cm_sp=plpafe-_-all-_-hard&an=linderholm%20carl&bi=h&sortby=17&tn=mathematics%20made%20difficult

Yep, that’s the one!

And there’s a “Mathematics Made Difficult” at the Braintree Public Library – much cheaper than ABE. I just put it on hold. Thanks for the reference, Mitch4.