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This Chinese Math Problem Has No Answer. Perhaps, It Has a Lot of Them. (washingtonpost.com)
Fifth-graders in China's Shunqing district were recently asked to answer this question: "If a ship had 26 sheep and 10 goats on board, how old is the ship's captain?" The Washington Post: The apparently unsolvable question sparked a debate over the merits of the Chinese education system and the value it places on the memorization of information over the importance of developing critical thinking skills. "Some surveys show that primary school students in our country lack a sense of critical awareness in regard to mathematics," a statement by the Shunqing Education Department posted Jan. 26 reportedly said. One student offered a pragmatic law-abiding answer: "The captain is at least 18 because he has to be an adult to drive the ship." Meanwhile on Twitter, some have gone with 42, a reference to the science fiction novel "A Hitchhiker's Guide to the Galaxy," by Douglas Adams, in which 42 is the "Answer to the Ultimate Question of Life, The Universe, and Everything." BBC: "If a school had 26 teachers, 10 of which weren't thinking, how old is the principal?" another asked. Some however, defended the school -- which has not been named -- saying the question promoted critical thinking. "The whole point of it is to make the students think. It's done that," one person commented. "This question forces children to explain their thinking and gives them space to be creative. We should have more questions like this," another said.
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.
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?
Don't believe me?
If 2.4 rounds down to 2 then What's 2.4 + 2.4? Why it's 2.8, which clearly rounds up to 3....
How about that kind of math question?
"File to fit, pound to insert, paint to match" - Aircraft Maintenance 101
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.
Sounds to me like a lot of people get angry when challenged.
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?
The Washington Post article links to a BBC article containing the following:
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.
Not enough information.
Y = 26S + 10G, solve for X.
Any other response would require a lengthy list of assumptions, the omission of which would make the answer automatically wrong. The captain needs to be at least 18 to operate a ship? That assumes that the captain is operating the ship legally, is operating the ship in an area where being an adult is required, is operating a type of ship that requires legally recognized captains, is a human ship operator and not a human, animal, or inanimate object bestowed with the title of captain in an honorary capacity, exists, etc. Even with all necessary assumptions, any single answer would be incomplete at best. Maybe a correct answer can be given by mapping out all of the possibilities and all of the assumptions associated with each, but the only certainly correct answer is that the problem cannot be solved with the information provided.
Purple, because aliens don't wear hats.
When I was in grade school, teachers would often make questions like these and often as the last on exams. This is not outrageous. This questions clearly helps the student asking them to examine the clues. If a plane crashes on the border of two countries, where are the survivors buried?
I thought common core was asinine...
I know the guy. Still owes me 10 bucks.
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.
... 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...
Shouldn't that be "20 sick sheep"?
If my post were a car, this sig would be its bumper-sticker.
Notice none of these reports, which are all sourced from a single fluff article from China, give the actual translation of the test question. Apparently not a single journalist reads Chinese? The wording is very important because if the original question started off with "You are the captain", then it is a trick/joke question with a correct answer. Instead, every article paraphrases the test question which completely distorts the story.
If it's one thing Chinese love, it's memorization based exams. They've been doing them for over a millennia.
This reminds me of the married couple handshake problem-
"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 solution to this one but it SEEMS like it shouldn't be possible to answer./P
Teacher: I... I dont knoAAARRRRRGGH
The answer to life, the universe and everything is the ascii value of the asterisk.
And Douglas Adams knew that.
The ASCII code for * is 42. Everything is the answer to Everything.
Nouvelles de jeux et technologies en français. TC
"There are 60 sheeps and ducks in total on the ship. Each sheep has 4 legs and each duck has 2 legs. How many sheeps are on the ship?"
I think this question is better, because it is not as obvious that the problem is unsolvable (I have to try this on real kids). A bonus point is that while the exact answer is impossible to calculate, you can calculate min and max values for the sheep count, e.g. "There are 0 - 15 sheep on board", which is often enough in work life, at least we do rough estimates all the time in my work.
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."
Imagine your driving a bus with 20 people on it.
5 get on, 3 get off
1 gets on, 6 get off
4 get on, 2 get off
12 get on, 7 get off
2 get on, 5 get off.
How old is the bus driver?
"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 still not too close to retirement, so I'll guess 50.
A dingo ate my sig...
Whoooooosh
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.
Every end has half a stick.
It isn't clear to me that this is a reasonable question for 5th graders, however if you are a little older and have a sense of how laws and meritorious promotion work you can start to create bounds for the problem. Min age for training for ships service, length of training, time to train and rise to rank of Captain. This involves looking at the class of ship, since we know it is transporting livestock we and start to focus on the training and parameters of that. There may be a maximum age as well, or an age where captains no longer captain but may be forced to take land based positions or act as harbor masters. There are a huge number of unknowns but you can build critical thinking skills and narrow the range of answers. Provided of course that there is some upfront knowledge in the field. You have to know that there are classes of ship, types and duration of training, periods spent in lower ranks. I don't know that this is a question for 5th graders unless they have close family that are very closely aligned with the field, or some relatively closely aligned field. Promotion to Captain may be akin to promotion in Military rank. Critical thinking? Perhaps, with a strong guiding hand. We don't know what the rest of the educational system is like. I would not expect a reasonable conversation out of the average 10 year old in a group setting.
If you have 1 bucket with 2 gallons and 1 bucket with 4 gallons, how many buckets you got?
rigged call in quiz show bus question
https://mikebattista.com/2009/...
The Cats on a Bus puzzle has the hallmarks of a Moon Logic Puzzle: "4 girls are travelling on a bus. Each of them have 3 baskets, in each basket there are 4 cats. Each cat has 3 little kittens. How many legs are in the bus?" note "222": The kittens were not on the bus, and the count included the driver's legs, and the legs of the seats as well
Here's another one: "4 girls are travelling on a bus. In each hand they hold 4 baskets, in each basket there are 4 cats. Each cat has 3 little kittens. One cat gets away. How many legs are on the bus?" note "1359": you begin to wonder what type of fuzzy math led to that
"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.
Inheritance is the sincerest form of nepotism.
have there been more total solar eclipses during a waxing moon or during a waning moon?
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 average age of ship captains, the average number of years captains have served, the average age people have children at etc.
That's how real life works. If you don't have any data relevant to answering the question then you either work on getting some related data or you put the question aside until some relevant data is available.
Comment removed based on user account deletion
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 observed? Perhaps the captain is operating in a country where 15 year olds can drive ships.
What kind of ship is it --- maybe this is a toy boat with toy goats and toy sheep in a bathtub? Who says the captain is driving this ship, anyways?
Critical thinking would be present an argument, or present a proposition question or claim or paper with information that contains flawwed reasoning and ask the students to analyze the paragraph and say whether they agree or not, and if there are any problems in what was written.
I would assume that this to be the case... Sheeps and goats.. Mothers and children maybe. Thats what they mean by critical thinking... outside the box
[($)]
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.
Richard Feynman on education in Brazil
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.)
lf(1): it's like ls(1) but sorts filenames by extension, tersely
When you fuck the neighbors' goats, do you line them up assembly line style or just jump the first goat that flick its tail in your direction?
...steadily rising for the past decade then how much does Donald Trump actually weight? Extra credit - given the average salinity of ocean water, will The Donald float? *duck and cover*
The original joke was: You are a captain of a ship. The ship has 26 sheep and 10 goats on board. How old is the captain?
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.)
Because this cargo is typical for the early 19th century, but not the 20th.
Following a robotics competition. They were interested in the differences between the approaches, every Chinese robot team had the same bot, and basically competed with tweaking the code optimizing speed. Efficient but not innovative. Our kids had bots that were not fast, but were playing out a half dozen HW/SW combinations, original construction, etc. Innovative but not efficient. They were intrigued. They attended our whole-school meeting, then on to the first session with a mixed grades 1-2 class. First up, show and tell. Student holding forth at one end of the room with his curated stuff, kids on carpet squares, teacher sitting on the table behind the kids. The visitors had a dozen questions about this. They would not have been more intrigued had the whole thing taken place on the ceiling. Later touring, they were interested in our 3D printers. They did not have these in their classrooms. I pointed out the irony that nearly every piece of these printers was made in China. They do have 3D printers now, IIRC they spec'd the same one for every school. We are now halfway through an exchange program, their kids came to learn with us this year, we'll go there next year. Sharing is good. Learning is good. The specific means should always be evolving.
Lewis Carroll famously posed this as an example of an unanswerable question, but people being unable to resist a challenge, some excellent answers have been given: "Poe wrote on both"; "They have inky quills"; etc. It's not about critical thinking; it's about creativity.
From the country that brought you "The sound of one hand clapping" comes a twist on the "there is no spoon" meme.
When they came for the communists, I said "He's next door. Take him away. Goddam commies."
Having no correct answer also implies there is no wrong answer, so everyone who answers the question gets it right.
"Would you know how to calculate the diameter of the globe?"
"No, I'm afraid I wouldn't," answered Schweik , "but I'd like to ask you a riddle myself, gentlemen. 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?"
The answer is your age, with an explanation of "I am the captain now.".
This person should be ignored in all decisions that have any importance.
Children should not be tested with questions that cannot be answered with the information available. If students in China are expected to know that you must have to have a boat license for 5 years to haul a certain amount of weight, and the average weights of those animals, then it's still an unanswerable question other than to say "greater than or equal to 28 years old". If these students are not expected to know that information, then this is beyond dumb and people thinking that it allows for "creative thinking" are non-critically thinking about the wrong subject.
Math does not need creative thinking. Math needs logic and structure. If you literally have to make up an answer, then it has nothing to do with Math.
The total temperature of the stars is (X + Y + Z) kelvin in an Algebra class. Feynman should know that's a valid answer.
Physicists more than any other science have to balance partial information. Both "Dark Matter" and "Dark Energy" are proposed solutions to balance out observed measurements.
On how much the essay aligns with the teacher's views.
My mother the valedictorian would be 105 now if she were still with us. She studied Math way back when 14" naval rifles were the ultimate weapon.
"If a battleship proceeding SE at 15 knots is 40,000 yds NNE of an enemy cruiser proceeding W at 14 knots, what is their distance of closest approach?" to which she would add "and what was the captain's name?".
I dislike teachers like you. Why? I show my work. You can see the lines on my face, the callouses on my hands, and the holes in my boots. But when I gave the landlord 9/10 of the rent, he still threw me out.
bad copy&paste and no QC
Hillary has lived in NY State for some 18 years now, which is longer than I've had this account.
The force that blew the Big Bang continues to accelerate.
"sparked a debate over the merits of the Chinese education system and the value it places on the memorization of information over the importance of developing critical thinking skills" - I would hope that would spark a debate over the merits of the US education system which does exactly the same damn thing.
Y+X=
This isn't worth talking about
n/t
Since farm animals are well established on every continent, there's generally no need to ship them this way. That implies that the captain is somehow just a bit crazy. This is not likely to be a profitable business, so he's doing it at a loss. Most likely he saved his money for some other purpose, but then was insane by the time he retired. Perhaps a year after retirement, he made all the arrangements to set sail on a ship full of farm animals for no good reason.
... Jimmy Saville groupie - OAP
Will someone please do the needful for the captain so he can leave with his sheep and goats?
Growing up I remember 5th grade math class had an entire chapter dedicated to questions like this you had to identify if there was too little information to solve the question.
They also had ones with frivolous information that you had to learn to filter out to answer the question correctly.
Questions like that were peppered in throughout my grade school curriculum. This was 80s and 90s in the US.
They missed the point of a very old joke question that starts with "Imagine you being the captain of a boat..."
If the captain is as old as the answer, then he is infinitely old (and the cargo is dead).
I use the creimer approach, I fill a bucket with lard and walk into the woods.
The goat that follows me, I marry it.
You thought I'd have premarital sex?
2 people are inside a closed room. There is nothing in the room except two black chairs and a white board. On the board is a big colored dot. Person A says the dot is green. Person B says the dot is blue. What color is the dot?
Sìshí'èr
the age of the captain problem has some modifications and variations which actually can be answered and also tests word problem understanding: one is: you are the captain of a boat in which 25 sheep and 10 goats are. How old is the captain? the captain problem is great the first time you see it. But again, once you have seen it, then it is still a template (and it is a 150n year old template). Solving it does not require any creativity any more. So, the pedagogical benefits are minimal. Except of course that if such a problem appears in an exam, it pisses off the majority of students.
If you don't give me enough data, I make my own shit up. Passive aggressive maths!
Task Mangler
We approximately the same question in a math class. We could not solve it. We eventually asked for the solution and was told that he was 27. After thinking a little more we asked how the teacher infered that. "I know the captain" was the explanation.
The article does not mention how the question was posted: in a written test, oral examination or debate.
If the student cannot get information from the questioner (written and oral exam), then the question is absurd, especially since it will be scored however subjectively. Also, 5th graders should not be concerned with valid ages for commanding ships. Here I can support the fight agains memorization (I always struggle with remembering unrelated/non-interesting things).
If it was in a debate, then I can accept it as a way to force the child to ask questions (you know, like IRL). This kind of curiosity can help memorize things (although with this question in particular I argue it's usefullness like in the point before).
Either way, scoring this question seems to be extremely subjective (a good student fails and a lucky one passes, or the teacher gives move information to some students than others).
If a school prioritizes teaching than scoring, then questions like these make sense (again, in a debate environment). However, the standardized teaching, which I assume occurs in most countries, needs a quantization of quality, thus it's results are based on scoring. A good example for this is all the IQ tests that ask me (from EU) US geographical or political questions. Intelligence is not memorization. Sure, more information may help intelligence, but more time should be spent processing than memorizing.
Actually I am from India and some time this type of lame, same or good question were asked by seniors, elders or teachers. The question start like this "Suppose you are the principal of the school and If a school had 26 teachers, 10 of which weren't thinking, how old is the principal?" This may be further added by other garbage information so that the child in question forgets that initially supposed to be the principal. So the answer is the "age of the person to whom we are asking the question." The purpose of such questions are how carefully you are listening and deducing the information further. This need not to be headline.
you end up with a shitty leader.
source: am american.
if your answer isn't insightful, doesn't advance thinking on the subject, or doesn't better society, it just isn't worth much.
Although I understand the purpose of the question, it is a math problem, so it should have a logical answer and a concrete result, otherwise call it is philosophy not math!
The captain is as old as his tongue and slightly older than his teeth.
(credits to Kris Kringle)
This is an example as to how to solve the problem.
We start with 26 sheep and 10 goats. When you're 16 years old, you're allowed by law to carry 5 sheep and 2 goats aboard. That leaves 21 sheep and 8 goats. You can carry an additional sheep every three years because they're taxed higher and that's the law. That makes seven years to carry that number of sheep. You can carry an additional goat per year, so that makes eight years. Everyone knows you'd carry the maximum, so it's 16 years old plus 8 years, making the captain 24 years old.
It's possible the math problem was created during a point when this was common knowledge in a village. Such a question would have been fair and not at all out of place. If it survived to this day, perhaps it did so in the context of a broader question, testing one's historical knowledge of that time period. It goes without saying that the question should be discarded if the context in which it could be solved is no longer valid.
A real teacher would focus on really useful skills.
This type of trick question is masterbastion by teachers who think they're smart while missing the point.
A teacher's obligation is to prepare kids for the real world, not to show them up with trick questions.
Seriously, that's childish.
My assumption was this was a play on the zodiac and we were supposed to give the range of ages the captain could be if they were born in the year of the goat.
Ergo sheep and goats
Old enough to get a commercial ship's master's license
Open-ended questions are great, but in order to answer you should have some idea of the domain of the desired answer. Am I meant to give the purely mathematical response, "There is not enough information"? Or to say "a non-negative number" because we know a living person's age must be a positive value? Should I specify more closely as "a non-negative real number" because I know an age can have fractional units and has no imaginary component? Am I meant to use my knowledge of the world to give a possible range -- "I know that you need to be 18 to be licensed as a ship's captain and the mandatory retirement age is 65, so the answer is bounded by those two values"? Is a probability wanted -- "Assuming a gaussian distribution of ages between 18 and 65..."? Or if it's a creativity exercise should we go a different direction and write a backstory for the captain, giving his age and motivations for captaining a ship full of livestock?
Hopefully the students had some guidelines regarding the sort of answer the exam was looking for.
Chelloveck
I give up on debugging. From now on, SIGSEGV is a feature.
Itâ(TM)s easy to answer both these correctly without any more information. Itâ(TM)s the same as âoehow long is a piece of string?â
Simple answer is the captain is twice as old as half his age.
This isn't like that because there is no relevant data. If it was "how many footballs can you fit in a swimming pool" there is relevant data, even if you don't have it to hand. You could even state it as something like ( L x W x H ) / D^3, and go on from there to discuss different forms of packing, whether you actually are packing them like atoms in a crystal or just chucking them in randomly, whether they're actual round footballs that you use with your feet, whether the water's been emptied out etc etc.
This is more like "What's the difference between a duck". Fucking rubbish.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
This is a type of question often used in job interviews.
-Eric