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## This Chinese Math Problem Has No Answer. Perhaps, It Has a Lot of Them. (washingtonpost.com) 443

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## This Chinese Math Problem Has No Answer. Perhaps, It Has a Lot of Them.

• #### There is always an answer (Score:5, Funny)

on Thursday February 01, 2018 @05:04PM (#56050099)
Asking questions for which there is insufficient data to determine the unique correct answer is confusing and a waste of time, because they will never see such questions in real life. Only teach them things they'll need in real life, I say. Don't fill their heads with nonsense. Every question they will need to answer in real life will have a correct answer, and they need to expect that from others.
• #### Re:There is always an answer (Score:5, Insightful)

on Thursday February 01, 2018 @05:29PM (#56050353)
I'm going to assume you're being incredibly sarcastic here because life is full of problems for which there is insufficient data to determine a correct answer. There are a great many that do already have good answers, but at one point there was insufficient data to answer them.

If you wanted to make this exercise more useful, I'd rephrase the question (to something that's not immediately obvious) and once they've figured out that they lack sufficient data, ask them what information they would need to produce an answer. Knowing that you have insufficient data to answer a question is one thing, but understanding what is missing and how to go about getting it is a highly valuable critical thinking exercise.
• #### Re: (Score:3, Funny)

by Anonymous Coward

You really need to mark this as sarcasm. Bear in mind that a lot of people reading this are from the USA...

• #### ...and a time to search for that answer (Score:2)

Asking questions for which there is insufficient data to determine the unique correct answer is confusing and a waste of time, because they will never see such questions in real life.

The difference is that in real life you usually have some data relevant to answering the question. If you don't then you go out and get something and infer the age of the captain from that. If you want to test critical thinking a better question would have included some details related to the age of the captain e.g. was s/he married, did s/he have kids and if so what were their ages, how big was the ship?, how many years had they been a captain etc. However then you would have need to provide data on the a

• #### Re: (Score:3)

There is a correct answer - but it is the set approximately {x|18x122}.
• #### Re: (Score:3)

I do this for work. Many of the problems I'm confronted with have no single, unique correct answer. It's a choice. In fact, this describes much application and computing system design.

But I do have a marginally useful amount of data, and some of it is in fact germane, so I'm not as bad off as 'If I have 600,000 users who need this feature, and it will cost \$1,000 per user to maintain it for another year, how much will it cost me to deprecate the feature and force those users onto another platform?'

Or maybe

on Thursday February 01, 2018 @05:05PM (#56050109)

If the question has no answer and is supposed to foster critical or creative thinking, how did the teachers grade the answers?
What were the actual answers? As it stands, this is bullshit "news" cause the important part of the whole incident wasn't reported. Why am I not surprised that it's "news" from Jeff Bezos' Blog?

Did the pupils get full credit when they pointed out how the question is unanswerable? Did they get credit for the lower bound of 18? Did they get no credit for things like the 42 answer which is simply a lame old joke?

• #### Re: (Score:2)

But it do have a answer.
If you know Chinese Law, you might know, to drive such a boat, with such a carge(more than X tons), you might require a special license, and that license requires some age to even certify for it. I think the answer is "Older than 26" or something.
But there is further value in there: If used properly, you can study and see how kids react in panic, since very few will know or guess anywhere correctly. Its also a question of reading: Do you understand that only some facts are irrelevant

on Thursday February 01, 2018 @05:51PM (#56050603)

The correct answer is: Méiyou zúgòu de xìnxi. (There is not enough information).

I used to live in Shanghai, and my (American) kids attended public schools there for several years. I was appalled at how much the math classes were based on drill, drill, drill with very little actual thinking. I am glad to see some "fuzzy" problems included.

There are some good things about Chinese math. For instance, in America teachers say "Show your work". In China, the teachers say "Do the math in your head, and only write down the answer". The teacher will call on kids to solve a problem written on the whiteboard, and make them do it with their hands behind their back. My kids can easily add up a column of numbers in their head, so when we eat at a restaurant, I always ask them to check the bill.

on Thursday February 01, 2018 @06:25PM (#56050879)

For instance, in America teachers say "Show your work".

This was my bane all the way through school, I like numbers and figured lots of mental tricks (natural to me) for solving things, and was familiar with lots of number patterns (like powers of two), and so much of time answers were obvious to me, but I was marked down for not "showing" the work I never did. They didn't want me to know how to find the answer, they wanted me to crank through a rote procedure. As a simple example, if you add stuff up in your head there is no work to show.

This even showed up in calculus when one old instructor wanted me to show my use of the "three step rule" for differentiation. What "three step rule'?! It appears that at some earlier time basic transformations for differentiation, which to me was a simple one step procedure, were divided into three separate "steps" for pedagogic reasons, I guess, which were entirely unnecessary, and not found in any recent text - basically manufacturing unneeded work.

by Anonymous Coward on Thursday February 01, 2018 @06:59PM (#56051111)

"Show your work" is shorthand for "prove you didn't cheat".
Just dropping down an answer means that as far as they can tell you copied it off a friend, looked it up online, etc.

on Thursday February 01, 2018 @08:39PM (#56051827)

"Show your work" is shorthand for "prove you didn't cheat".

That's part of it. "Show your work" also gives you partial marks if you had the correct reasoning but made a mistake somewhere along the way. It also reveals to the teacher if a large proportion of the class doesn't understand the same thing, so the teacher can concentrate on this.

But most of all, "show your work" is what real mathematicians do for a living. If you write a paper which says "the Goldbach conjecture is true, and I know because I proved it in my head", it will not get published because you need to show your work.

on Thursday February 01, 2018 @09:59PM (#56052231)

"Show your work" also gives you partial marks if you had the correct reasoning but made a mistake somewhere along the way.

NO!!! This is NOT what happens in America's schools. If this was all that happened, that would be fine. The problem is that that if a kid gets the correct answer, points are TAKEN AWAY for not "showing your work".

If a kid is confident in his ability, and doesn't want to fall back on the crutch of "partial credit", there should be no requirement to "show work". That is just punishing smart kids by forcing them to do it "the stupid way". Schools should not be in the business of making kids dumber.

on Thursday February 01, 2018 @10:32PM (#56052385)

The problem is that that if a kid gets the correct answer, points are TAKEN AWAY for not "showing your work".

Be sure to tell your reviewers that next time you submit a paper to an academic journal which is just a conclusion with no evidence for it. Maybe you'll get the lesson in the scientific method that your American school didn't give you.

BTW, you may have missed the word "also" in the sentence that you replied to.

on Friday February 02, 2018 @01:25AM (#56052985) Journal

Both happens in Germany.

Correct answer but not showing the way of calculation: only half the points. (Depending on school even 0 points)
Wrong answer, but correct calculation with some mistakes: 75% of the points.

Knowing HOW to do it is much more important than knowing the WHAT is the answer.

"That is just punishing smart kids by forcing them to do it "the stupid way". No it is not.
Every medical operation follows a standard, there is no "short cut".

The only "show me your work" where I agree is unnecessary is adding up some numbers.
But even then you can write:
sum of those is 120. s = 120.

And in further calculation write:
s * s is 14400

And so on.

Just writing 1,600,123 as result is as dumb and showing no sign of smartness as writing down a wrong way of calculating it.

• #### Re: (Score:3, Insightful)

If you write down 42 as an answer, the marker doesn't know if you guessed, if you just copied the answer out of the mark book, or if you actually worked it out. If you show the calculations then it's easier to tell these apart.

When you're teaching maths, you're not teaching people to get the right answer to a problem, you're teaching them to be able to get the right answer to all problems in a category. Seeing the answer lets the marker know if they've succeeded in the first objective, showing the work

on Thursday February 01, 2018 @07:02PM (#56051133)

The problem is that so many of those "intuitive" tricks that we build up in our heads are not actually true. We have no concrete proof that they're valid steps in the simplification of the problem. By demanding that you right down the steps you take, the teacher can point out when you take a step that doesn't actually hold up.

• #### Re: (Score:3)

That depends on the methods. Most people do large numbers on paper from right to left, but I can do it in my head in a sort of left to right blocking method. Take 56 * 27. I break that into the following steps:

(56 * 20) + (56 * 7)
1120 + (56 * 10) - (56 * 3)
1120 + (560 - 56 - 56 - 56)
1120 + (504 - 112)
1120 + 392
1512

In practice, it's not really different from the left to right method, except the numbers are easier for me to track in my head. YMMV, though.

on Thursday February 01, 2018 @08:28PM (#56051767) Homepage
I don't know what mental shortcuts you use, but I can prove that mine are valid.

Why would I write down 162 + 199 and add it up, when I can just mentally add 161 + 200?
Why would I do long multiplication of 50*49, when I can do (50*50)-50 in my head?

I once watched a class mate add zero to a number on his calculator. Can we accept that there are some mental shortcuts that are valid?

on Friday February 02, 2018 @01:36AM (#56053023) Journal

And why would you not write:
162 + 199 = 161 + 200 = 361? Takes no time.
And then you write: 50*49 = (50*50) -50 = 2450, takes no time either.

If you can do stuff in your mind, you can as well write down what you did in your mind, or not?
That is how I did it in school and no one complained.

on Thursday February 01, 2018 @07:10PM (#56051195)

I'm sorry to hear that. As an instructor, I always encouraged my students to show their work for an entirely different reason.

As I would explain: if you do the problem correctly, you will get full credit. If you get the problem wrong, I will go through the work you've shown and try to give you as much partial credit as I can justify. If you don't show much work, I can't give you any partial credit and so you'll get zero points on the question.

This is the only fair way to do it. Students that get 90% of a problem right should get 9/10 possible points. But to do that, you really do have to encourage them to show their work in sufficient granularity for the instructor to grade it.

• #### Re: (Score:2)

For instance, in America teachers say "Show your work". In China, the teachers say "Do the math in your head, and only write down the answer".

I hated that in grade school - I'd do additions by simply counting the numbers up in my head (much easier), then writing the answer down; of course, I wasn't "carrying the one's" so the teacher assumed I was using a calculator while doing my homework, so I had to start doing it "the stupid" way, with the little carries'n'crap so I wouldn't get marked down. Doing it this way was basically "drilled into" my head and took me a while to get it back out of my head.

by Anonymous Coward on Thursday February 01, 2018 @07:25PM (#56051285)

The correct answer is: Méiyou zúgòu de xìnxi. (There is not enough information)

No, the correct answer is today's date minus the captains date of birth.

• #### Re: (Score:2)

On how much the essay aligns with the teacher's views.

• #### Someone needs to turn this on the educators. (Score:3, Funny)

on Thursday February 01, 2018 @05:06PM (#56050127) Homepage

Fun fact: only some of the students will learn critical thinking skills from this exercise. All of them will completely lose any respect for authority or education though. Some of them will suffer permanent mental scarring because of it.

• #### the old LA one was more relevant (Score:5, Funny)

on Thursday February 01, 2018 @05:13PM (#56050179)

1. Johnny has an AK-47 with an 80-round clip. If he misses 6 out of 10 shots and shoots 13 times at each drive-by shooting, how many drive-by shootings can he attempt before he has to reload?

2. Jose has 2 ounces of cocaine and he sells an 8-ball to Jackson for \$320 and 2 grams to Billy for \$85 per gram. What is the street value of the balance of the cocaine if he doesn't cut it?

3. Rufus is pimping for three girls. If the price is \$65 for each trick, how many tricks will each girl have to turn so Rufus can pay for his \$800-per-day crack habit?

4. Jarone want to cut his 1/2 pound of heroin to make 20% more profit. How many ounces of cut will he need?

5. Willie gets \$200 for stealing a BMW, \$50 for a Chevy, and \$100 for a 4X4. If he has stolen 2 BMWs, 3 4X4s, how many Chevies will he have to steal to make \$800?

6. Raoul is in prison for 6 years for murder. He got \$10,000 for the hit. If his common law wife is spending \$100 per month, how much money will be left when he gets out of prison and how many years will he get for killing the bitch that spent his money?

7. If the average spray can covers 22 square feet and the average letter is 3 square feet, how many letters can a tagger spray with 3 cans of paint?

8. Hector knocked up 6 girls in his gang. There are 27 girls in the gang. What percentage of the girls in the gang has Hector knocked up?

9. Thelma can cook dinner for her 16 children for \$7.50 per night. She gets \$234 a month welfare for each child. If her \$325 per month rent goes up 15%, how many more children should she have to keep up with her expenses?

10. Salvador was arrested for dealing crack and his bail was set at \$25,000. If he pays a bail bondsman 12% and returns to Mexico, how much money will he lose by jumping bail?

• #### Re:the old LA one was more relevant (Score:5, Funny)

on Thursday February 01, 2018 @05:14PM (#56050189)

11. Bernie is a lookout for the gang. Bernie has a Boa Constrictor that eats 3 small rats per week at a cost of \$5 per rat. If Bernie makes \$700 a week as a lookout, how many weeks can he feed the Boa on one week's income?
12. Billy steals Joe's skateboard. As Billy skates away at 35 mph, Joe loads his .357 Magnum. If it takes Joe 20 seconds to load his magnum, how far away will Billy be when he gets whacked?

• #### Re: (Score:2)

For question 12, it is impossible to know precisely how far without knowing the mass of the bullets that were used and their type (a 357 can take about half a dozen different types of bullets, each moving at a different speed). Or are you only wanting to know how far Billy is at the time the trigger is pulled?
• #### Re: (Score:2)

Jarone? Come on now. All your other names were at least real. And I was expecting the 'Bernie' one to be about something something Venezuelan socialism.

• #### At least 28 years old (Score:5, Interesting)

by Anonymous Coward on Thursday February 01, 2018 @05:21PM (#56050249)

And of course, there's always that one person that has all the answers.

The total weight of 26 sheep and 10 goat is 7,700kg, based on the average weight of each animal," said one Weibo commenter.

In China, if you're driving a ship that has more than 5,000kg of cargo you need to have possessed a boat license for five years. The minimum age for getting a boat's license is 23, so he's at least 28.

• #### Re: (Score:2)

I'm not sure that problem solving is really equivalent to Sherlock Holmes level ability to memorize obscure reference material.

• #### Re: (Score:2, Insightful)

by Anonymous Coward

You don't need to memorize the material, but it is an extremely important lesson to learn that such material exists, and it's even relevant to advanced mathematics.

I don't remember most of my calculus days, but I do remember that most of my work consisted of trying random arbitrary approaches, and seeing which one advanced the problem toward the solution. Whether L'Hopital's rule, integration by parts, or other tactics I no longer remember, it's not always obvious how to proceed. Developing the skill to mat

• #### Re: (Score:2)

In China, if you're driving a ship that has more than 5,000kg of cargo...

Irrelevant. The captain doesn't "drive" the ship, the helmsman does. (Strictly speaking of course, the helmsman steers the ship and the captain tells the helmsman what course to steer and how sharp to make any turns.) How old you have to be to have a proper helmsman's license has nothing to do with the captain's age.
• #### Common Core has the answer... (Score:3, Funny)

on Thursday February 01, 2018 @05:23PM (#56050285)
Purple, because aliens don't wear hats.
• #### Re: (Score:3)

Unpatriotic lies! Of course you can buy tennis shoes on a Sunday in Oklahoma City.
• #### Fred Brooks interview question (Score:5, Interesting)

on Thursday February 01, 2018 @05:27PM (#56050337)
if it's really as intended. But it's probably a typo that didn't get caught. They happen. Feynman has a story in one of his books about finding a math problem like

Johnny observes three stars through his telescope. The stars' temperatures are X, Y, and Z kelvin. What is the total temperature observed?

when he was asked to evaluate science textbooks for the school board in Pasadena.

• #### Re:Fred Brooks interview question (Score:5, Insightful)

on Thursday February 01, 2018 @06:06PM (#56050749)

if it's really as intended. But it's probably a typo that didn't get caught. They happen. Feynman has a story in one of his books about finding a math problem like

Johnny observes three stars through his telescope. The stars' temperatures are X, Y, and Z kelvin. What is the total temperature observed?

when he was asked to evaluate science textbooks for the school board in Pasadena.

I looked at the original article which Feynman wrote and your summary, while extremely condensed and accurate enough for here, just assumes that the reader will get the point of Feynman's dislike of the question. I bet most here will miss it. The reason that Feynman objected to the question in the textbook is that in real life there is no reason at all to add the temperatures of stars, not that the question had a horrible mistake in it. That's very different from the question in the parent article, which is to test critical thinking.

• #### Re: (Score:2)

Fair enough. I guess I wasn't clear. My point was that individually sane thoughts like "add these numbers" and "Johnny did X" can get pasted together without filling in the necessary details in between, and that slips through the editing process. Here, for example, the missing information can be something like "In order to operate a boat with X amount of cargo, you need Y years experience; a goat weights Z kilos, a sheep weighs fifty percent more than a goat" that would have turned it into a real math probl
• #### Re: (Score:3)

Your point is mostly correct, but Feynman's reasoning was driven by an underlying scientific truth: temperature is not additive. Trying to add temperatures is actually mis-teaching about science.

Let me give you an example:

The average family income in America is \$50,000. For a Dutch family it is \$42,000. For a Chinese family it is \$9000. What is the total income? (Answer: \$101,000)

And it would be one thing to see such silliness in a math textbook, but would it be acceptable in an economics textbook?

• #### This question first appeared in 1841... (Score:5, Informative)

on Thursday February 01, 2018 @05:29PM (#56050359)

... and is known as the 'age of the captain' problem, introduced by Gustave Flaubert, a french writer.

It's been used to study how children in elementary school react to word problems. It has notthing to do with maths.

See e.g. https://www.jstor.org/stable/3... [jstor.org]

• #### Re: (Score:3)

Mod up please. This is exactly the kind of quality information that makes me read the comments before the article. The entire discussion makes no sense without knowing this. Shame on The Washington Post for publishing making this sound like some controversial idiotic thing, without providing the basic background!

• #### Re:This question first appeared in 1841... (Score:5, Insightful)

on Thursday February 01, 2018 @06:05PM (#56050739)

Mod up please. This is exactly the kind of quality information that makes me read the comments before the article. The entire discussion makes no sense without knowing this. Shame on The Washington Post for publishing making this sound like some controversial idiotic thing, without providing the basic background!

Perhaps I could help explain with a math problem. Seems fitting.

Since hype and bullshit are proven revenue streams, how many clicks and likes does it take to dismiss journalistic integrity and relevant information?

• #### It's all about enunciation (Score:2)

If a ship had 26 sheep...

Shouldn't that be "20 sick sheep"?

• #### Sometimes weird problems DO have solutions (Score:2)

This reminds me of the married couple handshake problem- [cut-the-knot.org]

"My wife and I recently attended a party at which there were four other married couples. Various handshakes took place. No one shook hands with oneself, nor with one's spouse, and no one shook hands with the same person more than once. After all the handshakes were over, I asked each person, including my wife, how many hands he (or she) had shaken. To my surprise each gave a different answer. How many hands did my wife shake?"

There is a nice elegant

• #### Re: (Score:2)

And still a pointless excercise.

• #### Re: (Score:2)

It's a good logic puzzle actually! I had fun figuring it out, when it was first presented to me.
• #### Re: (Score:2)

Except the solution provided is incorrect. It SEEMS correct, but it is not.
• #### Re: (Score:2)

Explain what is incorrect about the provided solution.
• #### Re: (Score:2)

It constructs a possible answer. But it asserts that 8 MUST be paired with 0. That is forgetting that my wife is a special case that breaks that logic. 8-0, 7-1, 6-2, 5-3, 4-me is indeed a legal answer (the one provided). So is 4-0, 7-1, 6-2, 5-3, 8-me.
• #### Re: (Score:3)

Among the five married couples no one shook more than eight hands. Therefore, if nine people each shake a different number of hands, the numbers must be 0, 1, 2, ..., and 8. The person who shook 8 hands has to be married to the person who shook 0 hands (otherwise that person could have shaken only seven hands.) Similarly, the person who shook seven hands is bound to be married to the person who shook 1 hand. So that the married couples shook hands in pairs 8/0, 7/1, 6/2, 5/3. The only person left who shook hands with 4 is my wife.

Except that there are two people at the party who shook no hands, apparently the question poser shook none also. So the actual pairings are 8/0, 7/1, 6/2, 5/3 and 4/0. His wife could be either the 4 hand shaker, or the 8 hand shaker, either way the answers satisfy the problem statement.

This logic puzzle requires unstated assumptions to derive the answer - which no logic puzzle should have. The question poser does not state that he is entirely excluded from the handshaking r

• #### It's the wildcard. (Score:2)

The answer to life, the universe and everything is the ascii value of the asterisk.

The ASCII code for * is 42. Everything is the answer to Everything.

• #### Project requirements (Score:5, Funny)

on Thursday February 01, 2018 @05:37PM (#56050453)

The question sounds like the quality of requirements documents I've been handed. Life is full of self-important people telling you to do the impossible with inadequate information, tools, time, and money. Sounds like the kids got an early insight into the "Joy of work."

• #### The principal is around 50 (Score:2)

"If a school had 26 teachers, 10 of which weren't thinking, how old is the principal?"

I think his or her age will be around 50. A young principal would have got rid of the non-thinkers, but this one has been around enough years that there is some kind of loyalty/blackmail thing going on with those 10 teachers. If he were closer to retirement, he would not be as worried about blackmail; he could push back for a short while until he got his retirement locked in.

So he or she has been there a long time, but sti

• #### Hasek's The Good Soldier Svejk (Score:2)

Take a three-storied house, with eight windows on each floor. On the roof there are two dormer windows and two chimneys. On every floor there are two tenants. And now, tell me, gentlemen, in what year the valet's grandmother died.

• #### It's like sort of like Idiocracy (Score:2)

If you have 1 bucket with 2 gallons and 1 bucket with 4 gallons, how many buckets you got?

• #### Isaac Asimov's response (Score:2)

"THERE IS AS YET INSUFFICIENT DATA FOR A MEANINGFUL ANSWER." - The Last Question
And adding unrelated lower case letters because the filter is wrong. The capitals are correct in the quotation.
• #### Unsuitable question (Score:2)

There is not enough information to resolve the question --- if you found something you say is an answer, then it was a mere guess or it wasn't through reasoning. This does not encourage Critical thinking; it encourages guesstaking and making unverifiable questionable assumptions and coming up with creative answers.

"The captain is at least 18 because he has to be an adult to drive the ship."

See, the question didn't provide any context to make that a reasonable proposition.
Who says the laws are being o

• #### Word problems as a test of understanding (Score:5, Interesting)

on Thursday February 01, 2018 @06:10PM (#56050785) Homepage

In one of Richard Feynman's books, he told about his experiences at a university in Brazil. He was horrified to realize that the students were ritually memorizing the course material with very little actual understanding.

When he asked questions in a way that echoed the textbook, students were able to recite an answer straight out of the book. But when he made up a "word problem" they were totally unable to answer.

A student was quizzed on physics, asked to compute what happens when light passes through a diamagnetic substance, and he recited the answer correctly and then calculated the correct result given the index and thickness of the substance. Immediately afterward, Feynman talked to that same student; Feynman held up a book and asked what would happen if the book was made of glass and he looked at something through the book. The student didn't realize that glass is a diamagnetic substance, and gave a very incorrect answer.

In the domain of math questions, I saw an example: if a person has 4 boards of length 2.5 metres each, and cuts them with a saw, how many 1-metre boards can that person make? Obviously the correct answer is 8 (two per board, with 4 left-over pieces of length 0.5 metres minus the width of two saw cuts). If you were just playing with the numbers abstractly you might think that since 4 * 2.5 == 10 that you could produce ten 1-metre board segments. You can't actually glue together 4 boards to make a single board, and you can't actually make zero-width cuts.

I can't speak for others, but I enjoy word problems more than abstract problems. (Good ones, anyway... you can take a simple problem and write an annoying and confusing word problem, and nobody likes those.)

• #### NaN (Score:5, Insightful)

on Thursday February 01, 2018 @06:47PM (#56051025)

This problem is not sufficiently bounded to solve from a mathematical perspective.

(That's the actual answer... You don't need to be over 18 if you are piloting the boat illegally and there may not even be a captain.)

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