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A cable of 80 meters (m) is hanging from the top of two poles that are both 50 m from the ground. What is the distance between the two poles, to one decimal place, if the center of the cable is:
I added part (a) since it is interesting mathematically. And I admit I did not solve it, but it was fun so I wanted to share. Watch the video for a solution.
Or keep reading. . .
“All will be well if you use your mind for your decisions, and mind only your decisions.” Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon.
. . . . . . M I N D . Y O U R . D E C I S I O N S . P U Z Z L E . . . . Answer To Amazon’s Hanging Cable Interview Question
(Pretty much all posts are transcribed quickly after I make the videos for them–please let me know if there are any typos/errors and I will correct them, thanks).
I didn’t remember how to solve this, and most of the references focused on physics concepts (weight, tension). Luckily I found a nice paper from Neil Chatterjee and Nita Bogdan with equations that made sense to me: The hanging cable problem for practical applications.
The setup is as follows. Due to symmetry, we can consider half the problem from one pole to the center. We can then double this distance for the distance between the two poles.
Also we will use a convenient coordinate system, centered at the lowest point of the hanging cable (which takes the shape of a catenary). We get the following “half diagram”:
The parameter a is unknown, and we want to solve for the value of x of the pole.
We also know that half of the cable length is 40 m, so using the equation for arc length of a catenary, we get another equation:
As this is half the hanging chain, the distance between the two poles is then double this value:
But if you try to solve this there is a problem. This equation has no solution! So what is going on?
If the cable is 80 m, then half of it is 40 m. But notice 40 m from the top of a 50 m pole is already 10 m above the ground. The cable therefore is hanging directly downward! The cable has to be doubled back upon itself, and the two poles must be coincident and 0 m apart!
This part is actually a trick question: the two poles are a distance of 0 apart. No physics was required to solve this one, just logical thinking!
Now an employee that uses common sense before wasting time with unnecessary calculations…I’d imagine that is probably an employee you want to hire.
I admit I did not solve this problem as I did not recognize the trick. But I like to learn about these problems, because it’s like the old saying goes.
Chatterjee, Neil, and Bogdan G. Nita. “The hanging cable problem for practical applications.” Atlantic Electronic Journal of Mathematics 4.1 (2010). http://euclid.trentu.ca/aejm/V4N1/Chatterjee.V4N1.pdf
I run the MindYourDecisions channel on YouTube, which has over 1 million subscribers and 200 million views. I am also the author of The Joy of Game Theory: An Introduction to Strategic Thinking, and several other books which are available on Amazon.
(As you might expect, the links for my books go to their listings on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.)
By way of history, I started the Mind Your Decisions blog back in 2007 to share a bit of math, personal finance, personal thoughts, and game theory. Its been quite a journey! I thank everyone that has shared my work, and I am very grateful for coverage in the press, including the Shorty Awards, The Telegraph, Freakonomics, and many other popular outlets.
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The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4.3/5 stars on 290 reviews)
40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.2/5 stars on 54 reviews)
The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.1/5 stars on 33 reviews)
The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.3/5 stars on 116 reviews)
Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 4.4/5 stars on 37 reviews)
Mind Your Puzzles is a collection of the three “Math Puzzles” books, volumes 1, 2, and 3. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory.
Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 112 reviews.
Math Puzzles Volume 2 is a sequel book with more great problems. (rated 4.2/5 stars on 33 reviews)
Math Puzzles Volume 3 is the third in the series. (rated 4.2/5 stars on 29 reviews)
Teachers and students around the world often email me about the books. Since education can have such a huge impact, I try to make the ebooks available as widely as possible at as low a price as possible.
Currently you can read most of my ebooks through Amazons “Kindle Unlimited” program. Included in the subscription you will get access to millions of ebooks. You dont need a Kindle device: you can install the Kindle app on any smartphone/tablet/computer/etc. I have compiled links to programs in some countries below. Please check your local Amazon website for availability and program terms.
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About Me: Presh Talwalkar
I run the MindYourDecisions channel on YouTube, which has over 2 million subscribers and 400 million views. I am also the author of The Joy of Game Theory: An Introduction to Strategic Thinking, and several other books which are available on Amazon.
(As you might expect, the links for my books go to their listings on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.)
By way of history, I started the Mind Your Decisions blog back in 2007 to share a bit of math, personal finance, personal thoughts, and game theory. Its been quite a journey! I thank everyone that has shared my work, and I am very grateful for coverage in the press, including the Shorty Awards, The Telegraph, Freakonomics, and many other popular outlets.
I studied Economics and Mathematics at Stanford University.
Feel free to send me an email [email protected]. I get so many emails that I may not reply, but I save all suggestions for puzzles/video topics.
If you purchase through these links, I may be compensated for purchases made on Amazon. As an Amazon Associate I earn from qualifying purchases. This does not affect the price you pay.
Book ratings are from January 2023.
Mind Your Decisions is a compilation of 5 books:
The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4.3/5 stars on 290 reviews)
40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 4.2/5 stars on 54 reviews)
The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias is a handbook that explains the many ways we are biased about decision-making and offers techniques to make smart decisions. (rated 4.1/5 stars on 33 reviews)
The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.3/5 stars on 116 reviews)
Multiply Numbers By Drawing Lines This book is a reference guide for my video that has over 1 million views on a geometric method to multiply numbers. (rated 4.4/5 stars on 37 reviews)
Mind Your Puzzles is a collection of the three “Math Puzzles” books, volumes 1, 2, and 3. The puzzles topics include the mathematical subjects including geometry, probability, logic, and game theory.
Math Puzzles Volume 1 features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 112 reviews.
Math Puzzles Volume 2 is a sequel book with more great problems. (rated 4.2/5 stars on 33 reviews)
Math Puzzles Volume 3 is the third in the series. (rated 4.2/5 stars on 29 reviews)
Teachers and students around the world often email me about the books. Since education can have such a huge impact, I try to make the ebooks available as widely as possible at as low a price as possible.
Currently you can read most of my ebooks through Amazon’s “Kindle Unlimited” program. Included in the subscription you will get access to millions of ebooks. You don’t need a Kindle device: you can install the Kindle app on any smartphone/tablet/computer/etc. I have compiled links to programs in some countries below. Please check your local Amazon website for availability and program terms.
Grab a mug, tshirt, and more at the official site for merchandise: Mind Your Decisions at Teespring.
If this problem is a breeze, see if you can solve this teaser for kids or this tricky brainteaser.
An interview with the tech giant will require applicants to not only answer questions but to solve tough math and logic-based problems as well, according to reports.
The Sun reached out to Amazon for comment on whether this and other similar questions are used in interviews.
A YouTube video allegedly posted by an Amazon hiring candidate outlines a math problem that candidates are supposedly asked to answer in the interview process.
YouTubers claim that the question originally came from a 2010 academic paper that was published in the Atlantic Electronic Journal of Mathematics.