Simple math questions stumping the internet

Media outlets around the world are reporting on these math problems that have "flummoxed" everyone. As these got so much attention, I wanted to share some of the headlines and give a small discussion about what I think is the real lesson of these problems.

Special thanks to emails that suggested these problems from Abhi (China problem) and Vinicius (dog show problem).

My blog post for this video

Sources and headlines around the world

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

South China Morning Post

The Portal (Chinese)

RT

BBC

Washington Post

Newsweek

Official response (Chinese).

Number of dogs question
"There are 49 dogs signed up to compete in the dog show. There are 36 more small dogs than large dogs signed up to compete. How many small dogs are signed up to compete?"

POPSUGAR

Daily Mail

New Zealand Herald

Forbes contributor Kevin Knudson (of "My favorite theorem podcast" fame)

My Favorite Theorem Podcast (just a link I recommend, nothing to do with these problems)

LADbible

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[Weerknuffelbeer]

This half-dog problem reminds me of another math joke I once heard... "Two mathematicians are taking a walk and see a house. They see 1 person entering the house and 2 persons leaving the house. Then one of the mathematicians says to the other: "Now 1 more person needs to enter the house and it's empty again.""

[jeffbrunton]

1) no mathematical answer

2) easy mathematically, not so easy for the dog in the middle

[davetye]

Reminds me of a joke:

A ship carrying a cargo of blue and red paint struck a remote island. The crew was marooned.

[Dhalin]

For the 2nd problem, I think what they *MEANT* to say is:

"There are 49 dogs signed up for a dog show. If there are 36 small dogs signed up for the show, how many large dogs were signed up for the show?" Because that would be a simple subtraction problem (13 is the obvious answer) which seems right for 2nd grade. I have my high doubts they expect a 2nd grader to bust out algebra equations, lol.

[sutfolsemaj]

Maybe there were 6 large dogs, 42 small dogs, and a Frankendog with the torso of a german sheppard and the head and legs of a chihuahua.

[kelsey]

What ever happened to answers like: "there is not enough information to answer this question, " or "data given is not applicable for the question?"
This sort of knowing when you don't have enough information was an important aspect of my elementary school math education.

[submandave]

Actually, it seems the answer to the second is 36 <= s <= 42. We are given a boundary on the total and a relationship between large and small. The values provided mean that there must be other dogs outside the ones given so we must account for all possible dog configurations.

[jongilbertson]

There are between 0 and 6 large dogs, between 36 and 42 small dogs, and between 1 and 13 medium dogs.

The ship's captain is old enough to know better.

[Anton]

I know a similar problem to 1):
Peter has 3 Apples, calculate the volume of the sun.

This question left me stomped.

[andrewpayette]

1) there is no answer.
2) typo

This was unfortunate

[Noximien]

When the media goes crazy about something like this, there really is nothing interesting happening anywhere that day.

[leandervr]

I think including questions like the first in a math test is great. Schools don't promote critical thinking enough. Teaching kids that sometimes the correct answer is 'I don't have enough data to answer this question' is exactly what's missing.

[wcbfg]

As someone from China, I've seen a "puzzle" like this: "You have a ship. There are X sheep and Y goats (or any number of any items) on the ship. How old is the ship’s captain?" The answer is your own age since it assumes you have the ship. But it's really a brain teaser rather than a math problem, and it seems unlikely to appear on a school exam.

[leonidsedov]

I think that in the first problem correct answer is "we have not enough data to draw any conclusion". And in the official answer they write about critical thinking. I believe it is critical enough to give the answer: "no answer".

[harmenbreedeveld]

The best answer to the Chinese question is: "I do not know the answer, as I do not have enough information.""

That would actually be a great insight: we don't know everything, we cannot know everything, and it is ok to admit that.

And it is an insight we do not teach enough at school, or in life.

[joseph-fernando-piano]

The second question reminds me of my 2nd year engineering thermodynamics final, one of the questions was calculating the efficiency of a given pump, but because of a typo in one of the temperatures, doing the problem correctly would give you an efficiency of over 900%... the professor realized this halfway through the exam, and made an announcement, so many of us went back and corrected the working... half an hour later, he made another announcement that they weren't technically allowed to make us do a problem twice, so just to leave it as it was and they would just mark based on the correct method... needless to say there were a lot of angry and stressed out students afterwards...

[KPkiller]

It really annoys me when the media writes posts about maths problems; they always convey that it is okay to be bad at maths and that maths is nonsense. I think it is people being exposed to this belief that really justifies in peoples' heads that they don't need to try. Then again, the media irritate me a lot of the time, I could be rambling about nothing.

[dcgreatman]

I did this from the thumbnail for like a solid 2 minutes wondering how there can be half a dog before finally clicking on the video and realizing it was a mistake.

[QemeH]

My high school chemistry teacher used to love these "quirky" text based exam question. They would always be something like: "Is hell exothermic or endothermic? Show your reasoning!" and only award extra credit/bonus points. A lot of my peers disliked those questions because they never had a definitive "right" answer, but I always went ham on them and put as much of my chemistry knowledge into the answer as I could. My favourite was the question where he had a murderer depose of a body using some sort of acid and asked what a CSI team could do to preserve as much as possible on arrival. I not only answered that, but I also made a comment about how the murderer shouldn't have used acid, but rather lye as it was both easier to aquire, less detectable and harder to counteract afterwards. (Or something similar, it's been a hot minute since high school... -.-)

[JeremyMcCandlish]

"What about medium-sized dogs?"

Love it.

36 <= s <= 42