Posted March 27, 2016 By Presh Talwalkar. Read about me , or email me .

Source Fiske, Edward B. “A Second Student Wins Challenge on Answer To Math Exam Problem.” New York Times. 24 March 1981. Accessed online. http://www.nytimes.com/1981/03/24/nyregion/a-second-student-wins-challenge-on-answer-to-math-exam-problem.html

The test-makers did admit the error and they gave 10 extra points to the roughly 1/4 of students who had chosen (C).

In particular 4 is a square of the integer -2, because 4 = (-2) 2 ; and the number 8 is the cube of a different integer 2 because 8 = 2 3 . So answer choice (C) is also a valid response.

In fact, (C) is a correct answer. The question is not limited to positive numbers. The question asks about integers, which could include both positive and negative numbers.

But look again at answer choice (C). The test-makers probably included this row as a distraction. It is true that 4 is a square since 4 = 2 2 and 8 is a cube because 8 = 2 3 . But both 4 and 8 involve the same number 2 which is supposed to invalidate this choice answer.

The correct answer was supposed to be (B) because 9 = 3 2 and 8 = 2 3 . The number 9 is the square of 3, and the number 8 is the square of a different integer 2.

Which row contains both the square of an integer and the cube of a different integer?

"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 .

Or keep reading for a text explanation. . . "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 Can You Spot The Error In This Test Question?

On the SAT there is only supposed to be one correct answer. However the test-makers make a mistake on this question. Can you figure out what they did wrong?

Which row contains both the square of an integer and the cube of a different integer?

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.

People often ask how I make the videos. Like many YouTubers I use popular software to prepare my videos. You can search for animation software tutorials on YouTube to learn how to make videos. Be prepared--animation is time consuming and software can be expensive!

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. It's 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.

(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.)

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 .

MY BOOKS

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.

Mind Your Decisions is a compilation of 5 books:

(1) The Joy of Game Theory: An Introduction to Strategic Thinking (2) 40 Paradoxes in Logic, Probability, and Game Theory (3) The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias (4) The Best Mental Math Tricks (5) Multiply Numbers By Drawing Lines

The Joy of Game Theory shows how you can use math to out-think your competition. (rated 4.2/5 stars on 116 reviews)

40 Paradoxes in Logic, Probability, and Game Theory contains thought-provoking and counter-intuitive results. (rated 3.9/5 stars on 21 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 3.6/5 stars on 10 reviews)

The Best Mental Math Tricks teaches how you can look like a math genius by solving problems in your head (rated 4.4/5 stars on 26 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 4.5/5 stars on 16 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 4.5/5 stars on 32 reviews .

Math Puzzles Volume 2 is a sequel book with more great problems. (rated 4.5/5 stars on 10 reviews)

Math Puzzles Volume 3 is the third in the series. (rated 4.5/5 stars on 8 reviews)

Amazon.com Prime Reading

I am thrilled to announce my ebook 40 Paradoxes in Logic, Probability, and Game Theory was selected for the Amazon.com Prime Reading program! Right now Prime members can read the book for free. Go to the Prime Reading catalog and find my book "40 Paradoxes in Logic, Probability, and Game Theory" and select the option to borrow for free.

Prime Reading

Be sure to read it soon! The promotion is valid for about 90 days, starting March 18.

Here is a link to the book's main page:

40 Paradoxes in Logic, Probability, and Game Theory

You don't need a Kindle to read the ebook. You can install the Kindle app on virtually any computer/smart phone/tablet/etc.

Amazon.c Prime Reading

I am thrilled to announce my ebook The Joy of Game Theory was selected for the Amazon.ca Prime Reading program! Right now Prime members in India can read the book for free. Go to the Prime Reading catalog and find my book "The Joy of Game Theory" and select the option to borrow for free.

Prime Reading

Be sure to read it soon! The promotion is valid until 22 December 2020.

Here is a link to the book's main page:

The Joy of Game Theory

You don't need a Kindle to read the ebook. You can install the Kindle app on virtually any computer/smart phone/tablet/etc.

KINDLE UNLIMITED

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.

MERCHANDISE

Grab a mug, tshirt, and more at the official site for merchandise: Mind Your Decisions at Teespring.