'Unsolvable' exam question leaves Chinese students flummoxed | Hacker News Reader

'Unsolvable' exam question leaves Chinese students flummoxed

bbc.com

43 pointslnguyen61 comments

Growing up in the US, we used to have questions like this on math exams. The correct answer is something to the effect of "Not enough information to solve this problem". Of course we had practice questions where that was the case before the exam, so it wasn't a surprise or anything... but it was standard practice.

Questions like "A ball is fired from a cannon at a 45 degree angle, how far from it's initial position does it land?" are also fairly common in Canada. I don't recall every being asked something this silly though. There's no formula to calculate the age of a ship captain based on his cargo. There's no 'missing piece' here.

Without the "it's", I trust.

Read the article - there are several clues, and bounds can be calculated.

I read the article. The question is stated to be

> "If a ship had 26 sheep and 10 goats onboard, how old is the ship's captain?"

What 'clue' did I miss? The only other information is some speculation from a Weibo commenter who thinks that 26 sheep + 10 goats = 7700kgs.

I supposed you could argue that these 5th grade students should know the minimum age required to have a commercial boat licence, but I couldn't tell you that answer for my country (and we don't know that this is a commercial ship, could just be someone taking his livestock for a jaunt around the lake).

Scroll past the ads. There's lots more.

No, there isn't. Please quote what other information is provided.

The other information, is the reasonable assumption that there is a minimum age limit for getting a license, and an apprenticeship for larger vessels. As mentioned. Even if you don't know the numbers, you can sketch out that thought process for an answer. Not all algebra is done with constants.

In fact my sister ran the data systems for a large trucking company. Her interview questions included "how many ping pong balls will fit in a semi-truck trailer?" She was looking for any kind of process to arrive at an answer. Most folks just flailed around, helpless because the question didn't include the answer in it (like so many test questions in school).

There still isn't an answer to the problem.

Sure - in the form of bounds (older than...younger than).

This is all about students being taught by rote, with right answers all neat and pat and solvable. Folks educated like that have a problem with questions like this one. Folks who can 'think outside the box' have no issue at all with uncertainty in the answer.

Similarly, folks posting here who can or cannot see that this question is interesting and solvable (do a degree). No, not by 'an answer' but by a variety of approaches.

How many 11 years olds could "sketch out that thought process [about an apprenticeship] for an answer"?

I certainly couldn't have done that.

One of the answers was "must be an adult", which still sets bounds. That sounds like a much more reasonable answer for an 11 year old, while it sounds like you think it's reasonable to require a tighter range. Why?

> Folks who can 'think outside the box' have no issue at all with uncertainty in the answer.

Folks who can "think outside the box" can conceive of a world where "there is no answer to this question" is a meaningful response.

Rather than needing to know the probable weight of 26 sheep and 10 goats is 7700kgs, you need to know by what margin of error it's probably over 5000kg. And you not only need to know the minimum age of 28 yrs, but also the probable age distribution of people with commercial boat licences, in both China and other countries. Along with knowing risk factors such as piracy rates in areas of the world where live sheep and goats are transported, you can combine all this info into a statistical model useful for actuarial purposes. Perhaps the exam question was searching for primary school kids to fast-track for a career in China's growing Insurance industry.

"There's no formula to calculate the age of a ship captain based on his cargo. There's no 'missing piece' here."

The lack of relevant relationship is the missing piece.

Given how much nonsense I've personally witnessed as a math tutor or TA as students shove unrelated numbers through unrelated equations in unmotivated manners in an attempt to come up with some answer, any answer, I'd say it's not any worse a question than giving them one that does correspond to an equation but has too few terms nailed down for a concrete answer.

The weird part of this story to me is that it is somehow newsworthy. Is it truly such an oddity in China that this made it to international news, or is there a heavy dollop of our local media basically turning off their critical thinking when it comes to China or Japan and boggling at anything, no matter how mundane?

Discovery of Jesus on french toast in mexico ignites local flames of monotheistic debate has caught the attention of the nation, and potentially, the entire planet

I certainly sure that they've read something about this in the U.S, and they thought it would be a good idea to try the same thing. I'll bet it was a direct copy from the U.S.

The problem is sometimes mistakes happen in exam questions, from simple typos to impossible questions, etc. How is the student to know that this was a genuine question vs. a mistake?

How can it matter? If its unanswerable, its unanswerable for everyone.

that is the correct answer

Then there are the questions that, at first sight, do not seem to have all the information, yet they do. Consider the one that opens this article:

http://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.h...

What's interesting about that problem is that (for me, at least) knowing that that is enough information to solve it makes solving it a lot easier. If I was just told to make as much headway as I could, I'd get stuck on some tricky geometry, but once you're told that the answer is a single number, not in terms of any variables, the method of solution became clear.

> Then there are the questions that, at first sight, do not seem to have all the information, yet they do.

I love the following problem, in a similar vein:

There are two chosen natural numbers x and y, both between 1 and 100. Two smart people, Alice and Bob, are told this fact, and Alice is secretly told x*y, and Bob is secretly told x+y, and they are also told who knows what. Then the following conversation happens:

Alice: I don't know the two numbers.

Bob: I knew you wouldn't know them.

Alice: Now I do know the two numbers.

Bob: And now I do know them as well.

The question is, what are the two numbers?

4 and 13

Before anyone else gets lost trying to solve this, the parent posted the puzzle incorrectly.

The correct limits on the numbers are that: - Each of them is greater than 1, but their sum is less than 100

Still not all the information according to this link: https://en.wikipedia.org/wiki/Sum_and_Product_Puzzle

y > x is the last constraint

That constraint is not necessary as the problem only asked for the two numbers, not the values of x and y respectively.

It sounds like the old programming interview questions: "Why are sewer covers round?", etc. They sound like they promote critical thinking, but really they just confuse the applicants. If you want to know how someone thinks, ask them to solve a problem step by step.

Such questions are usually shibboleths for cultural and social affinity, rather than objective attempts to test critical thinking and logic.

An upvote for using the word "shibboleth."

Asking them to solve a problem step by step is great to learn whether that person is good at explaining the solution step by step. It is not about internal thought process you use to come up with solution.

Well, they have to at least be able to solve the problem, and being able to explain a solution is an important skill in its own right. Unless you are researching thought processes, or you are a Hardy working with a Ramanujan, the distinction you are making does not matter a whole lot.

I strongly disagree. If that happens then the interviewer is not doing their job.

You don't ask the applicant to solve and then explain, you ask them to solve and think aloud while they do it. If this doesn't come naturally to the candidate, which is totally fine, you must ask questions, suggest doubts, propose alternatives or request clarifications to encourage thinking aloud.

If you realize the candidate already knew the solution and is in fact just explaining it, then you have failed to prepare a sufficiently interesting question, and must come up with another.

I was always pretty good at these questions, honestly enjoyed them and I would never tell you my actual thought process. Of course I would answer questions (which are basically fun side quests), but especially if you interrupt me with them, you are not getting anything remotely resembling my thought process. You have me answering your questions and my thinking+behavior are heavily influenced by them and by what I see in socially appropriate behavior.

Sounds totally reasonable because 95% of the time software developers simultaneously write code and speak loudly about what they're doing at each step, while some timer is ticking in the background. Oh, wait...

i only know from learning about it, but round manhole covers prevent them from falling through the hole by consisting of a curve of constant width. Another example is the Reuleaux Triangle which is a viable shape for manhole covers. https://en.m.wikipedia.org/wiki/Reuleaux_triangle

not exactly a great logic question

The problem I have with this question is that it’s based on false pretenses. Plenty of manhole covers are not round.

Cool! I didn't know this was a thing, but I came up with the same solution independently when asked this question.

It also makes a wheel that has a constant tangent from the ground (not a constant axel point) as it turns.

> "Why are sewer covers round?"

Because sewer access holes are round.

Because the manufacturer was cutting corners. ;-)

I read once that "Wendy's restaurants" used square burgers instead of round because they "don't cut corners".

http://www.businessinsider.com/why-are-wendys-burgers-square...

The are squared sewers holes all around the world. At least, in front of my house, next to workplace and I encountered multiple others on my way between work and home today.

It's a Kobayashi Maru. They're supposed to demonstrate their hacking skills and change the exam score.

It’s worth pointing out that the intent of the Kobayashi Maru is to present the candidate with the terror, trauma, and experience of inevitable doom. Kirk cheated brilliantly, but that was not the point.

It's a classic nonsense word problem, first appearing in 1841: https://en.wikipedia.org/wiki/Age_of_the_captain

It's also been used to examine how students react to nonsensical word problems, and this is to some extent backed up by the school's statement. However, given the reputation of Chinese schools, it's entirely possible the teacher preparing the test simply threw it in because it looked like a word problem and the school is just saving face.

> However, given the reputation of Chinese schools, it's entirely possible the teacher preparing the test simply threw it in because it looked like a word problem

Action: Chinese school tries to break stereotype.

Result: stereotype reinforced, because people would rather believe that than the explicit explanation.

Back in school professors used to add goofy questions like this, which could only be answered if you actually attended the classes. It was a way to account for diligence, according to the professor anyway.

This sounds like a messed up variant of an actual solvable old riddle that goes something like:

"Imagine that that you are the captain of a ship, there are 26 sheep and 10 goat on board... "

... go on for about 2 minutes talking about how the ship stops in different ports and how number of respective animals change... Add another animals as well, make the listener assume that they need to keep the count in their head...

"Now in the final destination all of the animal get off the ship. How old is the ship's captain?"

(Ok, I will be that guy.)

So what is the solution?

Your age.

Ah. This is a nice one, I will try on my children - hopefully they will be brighter than their dad.

The younger was :)

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

Those are some MASSIVE sheep. I like that the internet know it all was just as wrong as everyone else. Also that the writer of the article didn't even bother to fact check it.

That's like a question that might appear as a gag in a SNL final exams skit. I'm for the odd unconventional question that might not follow a premise that was well-established in class per se (used deliberately, and sparingly)...but not a question which can only result in confusion and frustration.

Except that's life.

Here's my answer to that question:

Risky Business(1983):

Miles: Sometimes you gotta say "What the F*ck", make your move.

This is my favorite unsolvable exam question! (Single page pdf)

http://nuclear.ucdavis.edu/~tgutierr/files/sml2.pdf

That's not unsolvable: https://www.symmetrymagazine.org/article/the-deconstructed-s...

40 sheep isn't 7700 kg, I don't think. that's 400 lb per sheep.

Bob is looking at Mary, but Mary is looking at Ed. Bob is married but Ed is not. Is a married person looking at an unmarried person? a) Yes b) No c) Not enough information to say

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

Well that's just not true.

Maybe they meant pounds? Large sheep can weigh around 250lb so it gets closer to the 7700 number

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