# 10 viral math equations that stumped the internet

• A viral math equation with two solutions confused Facebook users.
• A seemingly simple math problem went viral on YouTube because of two different versions of the order of operations.
• The way a teacher graded a Common Core math quiz caused a firestorm on Reddit.

Math comes naturally to some, but even simple equations remain baffling brainteasersto others.

These math equations went viral for being much more complicated than they seemed — or so simple that people got tripped up overthinking them.

Here are 10 math problems that confused people across the internet.

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## This viral math question has two solutions.

Spotted on The Daily Mail, the question was originally created by Go Tumble and shared on Wikr before taking off on Facebook and going viral.

There are two correct ways to solve it. The first way to find the solution is to add the equation, then combine the sum with that of the previous equation. The second solution involves multiplying the second number of the equation by the number you are adding to it. The correct answer could either be 40 or 96.

Here’s a full explanation of the answer. There are two ways to solve this math problem that’s going viral online.

### The INSIDER Summary:

• This math equation is sparking a debate on Facebook.
• With two possible answers, no one can decide which answer is correct.
• Do you have what it takes to find them both?

Do you feel pretty confident in your math skills? If so, you may want to peruse the math question that has people on Facebook freaking out over it’s two possible solutions.

Spotted on The Daily Mail, the question was originally created by Go Tumble and shared on Wikr before taking off on Facebook.

The creator of the riddle-slash-math-question notes that this isn’t a simple equation, and it requires some creative thinking.

“Firstly, think outside the box! This math riddle is not that simple,” the user writes. “Even though there’s usually one right answer for math problems, two common solutions are causing heated debates all over the world!”

### Solution 1: Add the equation, then combine the sum to that of the previous equation.

Let’s do this together.

First line: 1 + 4 = 5

Second line: 2 + 5 = 7. So add the first sum of the previous equation, like so: 5 + 7 = 12

Third line: 3 + 6= 9, so add 9 + 12 = 21.

Solution: 8 + 11 = 19, so add 19 + 21 = 40.

40 is a widely accepted and correct answer. However, it’s not the only correct one.

### Solution 2: Instead of just adding, this second solution involves multiplying the second number of the equation by the number you are adding to it.

First line: 1 + (4 x 1) = 5

Second line: 2 + (5 x 2) = 12

Third line: 3 + (6 x 3) = 21

Solution: 8 + (11 x 8) = 96

So either 40 or 96 are correct answers to this question. Consider our minds blown.

## This seemingly simple math problem racked up over five million views on YouTube.

The correct way to solve this problem is to use the modern interpretation of the order of operations, also known as PEMDAS or BODMAS:

• Parentheses/Brackets
• Exponents/Orders
• Multiplication-Division
• If same precedence, left to right

The correct answer is 9, but controversy ensued because the historical order of operations from before 1917 differs slightly. With that version of the rules, which is still taught in many schools, the answer would be 1.

Here’s a full explanation of the answer.

## This Common Core math quiz caused a firestorm on Reddit.

The first question asks the student to calculate 5 x 3 using repeated addition. The student wrote 5 + 5 + 5 = 15, and was marked wrong, with the teacher writing in the “correct” solution of 3 + 3 + 3 + 3 + 3 = 15.

The second question prompts the student to calculate 4 x 6 using an array. The student drew an array with six rows and four columns, getting the answer that 4 x 6 = 24. The teacher marked the question wrong again and drew in a nearly identical array of four rows and six columns.

“The idea that a student should be punished for recognizing and applying the fundamental truth of commutative multiplication in service of drilling in a completely arbitrary convention that they can easily learn when they need it 10 years later strikes me as borderline insane,” Andy Kiersz of Business Insider wrote.

# The ‘Common Core’ math quiz that has everyone outraged isn’t about Common Core – it’s worse

A bafflingly graded third grade math quiz caused a firestorm on Redditlast week, and has spread across the internet, causing several people to question Common Core math standards and the teacher’s implementation of them.

The quiz is on some of the most fundamental aspects of basic whole number multiplication and how students encountering multiplication for the first time can think about problems.

The first question asks the student to calculate 5 x 3 using repeated addition. The student wrote 5 + 5 + 5 = 15, and was marked wrong, with the teacher writing in the “correct” solution of 3 + 3 + 3 + 3 + 3 = 15.

The second question prompts the student to calculate 4 x 6 using an array. The student drew an array with six rows and four columns, getting the answer that 4 x 6 =24. The teacher again marked the question wrong, and drew in a nearly identical array of four rows and six columns:

This, naturally, has a lot of people pretty riled up. Here’s what’s going on.

It is obvious to anyone who looks at this problem that the student did precisely what was asked. For the first question, they interpreted multiplication as repeated addition. For the second question, they went with a graphic interpretation of multiplication, looking at a stylized version of finding the area of a rectangle.

One of the most basic properties of whole number (and integer, rational, real, and complex number, along with many more) multiplication is commutativity: for any two numbers A and B, A x B = B x A. Order does not matter in multiplication; adding five together three times is exactly the same as adding three together five times.

To a third grader just encountering arithmetic for the first time, that might not be immediately obvious. This actually gives one of the strengths of looking at more visual illustrations of multiplication like the arrays in the second problem: Many students will very quickly see that an array with four rows of six columns has the same size as an array with six rows of four columns.

A teacher penalizing a student for recognizing and applying commutativity is extremely harsh and unwarranted. One possible rationale for the grading scheme could be a formalistic issue: The curriculum or teacher might have formally defined multiplying together two whole numbers A and B as the total number of objects in a collection of A groups of B objects each. In that case, 5 x 3 would be defined officially to be 5 groups of 3, or 3 + 3 + 3 + 3 + 3.

It still makes no sense to penalize that student, even in this case. Commutativity is one of the first properties that emerges from that definition, and the student is still, in both problems, capturing the essence of what multiplication is.

## This is NOT a Common Core standard

This example, along with so many other viral math problems that baffle students and parents (like this subtraction problem, or this check mocking a first grade counting exercise), is being used as an example of Common Core math being unduly confusing or frustrating.

While this worksheet does present a frustrating situation, it has nothing to do with Common Core. Common Core lays out a set of objectives for what students should be learning in each grade level. It’s still up to individual states, districts, and teachers to come up with the specific curricula and lesson plans to achieve those objectives.

As New York City high school math and physics teacher Frank Noschese told Tech Insider’s Madison Malone Kircher, “The standards just lay out what kids should know and be able to do, not actual lessons. Nothing in Common Core forces the specific interpretation these teachers used.”

The two Common Core standards listed at the top of the quiz ask students to “interpret products of whole numbers” and to “use multiplication and division within 100 to solve word problems.” Absent from those standards is an insistence on slavish devotion to a pedantic hyper-formal definition with no particular mathematical meaning.

Indeed, penalizing the student for their recognition that 5 x 3 = 5 + 5 + 5 just as much as it does 3 + 3 + 3 + 3 + 3, or that a grid with six rows and four columns is the same size as one with four rows and six columns, goes against the deeper spirit of much of the Common Core math standards: to reinforce a fundamental understanding of what numbers and operations are and how they interact with each other to provide a solid foundation for further mathematical study.

However this grading mishap happened, it wasn’t Common Core’s fault.

## This has nothing to do with higher order math

One explanation that was floated by several Redditors (ninjakiti here is one example) and blogger Hemant Mehta revolves around the fact that for arrays in computer science and matrices in linear algebra, order does matter.

The idea is that, in the second problem, an array or matrix with four rows and six columns is in fact a very different thing than an array or matrix with six rows and four columns. It’s conventional to describe the dimensions of a matrix by putting the number of rows first and the number of columns second. In that case, the 4 x 6 array asked for on the quiz would be different than the 6 x 4 array the student drew.

I do not think this is the solution here for two reasons.

First, this is a problem involving basic single-digit whole number multiplication. It is likely one of the first times students are encountering multiplication. Students are unlikely to encounter matrices until their later high school years, and it would seem a rather odd pedagogical choice to enforce a convention in linear algebra and computer programming that students aren’t going to see for nearly a decade, without any explanation of why that convention matters, at the same time students are expected to grasp the most basic properties of integer multiplication, like commutativity.

Second, commutativity is a bedrock mathematical fact, while matrix dimension notation is an arbitrary convention. One of the very few things I am willing to accept as an absolute, immutable, universal truth that holds in all times and places is that the order in which two whole numbers are multiplied together does not matter. 5 x 3 = 3 x 5 is written into the fundamental fabric of reality in a way very few other things are.

Meanwhile, describing matrices as rows by columns is essentially arbitrary. We could have just as easily chosen to write them as columns by rows. As it happens, modern mathematics settled on the former rather than the latter. This is similar to how English is read from left to right, while Arabic is read from right to left. Neither of those are fundamental, inevitable aspects of these languages; they are just how things worked out.

The idea that a student should be punished for recognizing and applying the fundamental truth of commutative multiplication in service of drilling in a completely arbitrary convention that they can easily learn when they need it ten years later strikes me as borderline insane.

### NOW WATCH: Why ‘5+5+5=15’ is wrong under the Common Core

Here’s a “repeated addition” Common Core problem that’s taught in third grade in US schools:

Use the repeated-addition strategy to solve 5×3.

If you answer the question with 5+5+5=15, you would be wrong.

Mathematically, both are correct. But under Common Core,you’re supposed to read 5×3 as “five groups of three.” So “three groups of five” is wrong.

According to Common Core defenders, this method will be useful when students do more advanced math. This way of reading things, for instance, can be used when students learn matrices in multivariable calculus in high school.

But parents aren’t happy about it.

Story by Jacob Shamsian and editing by Ben Nigh.

## This math problem from Singapore went viral in the US.

Kenneth Kong, a television host in Singapore, shared a photo of this 5th grade-level math question in a since-deleted Facebook post, which was shared nearly 6,000 times.

In the logic puzzle, Cheryl gives her friends Albert and Bernard different clues as to when her birthday is out of a selection of dates. She tells Albert only the day and Bernard only the month of her birthday.

By making a table of the dates and using the process of elimination, one can determine that Cheryl’s birthday is July 16.

It was later revealed that this problem wasn’t a regular test question used in Singapore classrooms. It was actually used in a contest as part of the Singapore and Asian Schools Math Olympiad (SASMO).

The New York Times published a detailed explanation of the solution, which you can read here.

Otherwise, this answer will be even more confusing.

This genre of logic puzzles is baffling in large part because people rarely act this way. The puzzles also have built-in assumptions — everyone is truthful, for instance and no one gets offended and walks off when strangers insist on making basic communication so complicated. Students who compete in math competitions are generally familiar with the conventions of logic puzzles, but people who have not taken a math class for more than a decade generally say, “Huh?”

This puzzle is particularly convoluted. Why don’t Albert and Bernard just blurt out what Cheryl has told them? Why is Cheryl so coy about revealing the month and day, but not year, of her birthday? What else is Cheryl trying to hide?

But if you are willing to play, here’s how the logic unwinds.

It helps to put the list of 10 dates into table form:

Now let’s examine what Albert and Bernard say. Albert goes first:

I don’t know when your birthday is, but I know Bernard doesn’t know, either.

The first half of the sentence is obvious — Albert only knows the month, but not the day — but the second half is the first critical clue.

The initial reaction is, how could Bernard know? Cheryl only whispered the day, so how could he have more information than Albert? But if Cheryl had whispered “19,” then Bernard would indeed know the exact date — May 19 — because there is only one date with 19 in it. Similarly, if Cheryl had told Bernard, “18,” then Bernard would know Cheryl’s birthday was June 18.

This second grade math question stumped kids and their parents.

A UK mom tweeted this math problem in a since-deleted tweet saying “Have you seen this one? Year 2!!” It was then picked up by a Facebook page called Parents Against Primary Testing and media outlets like The Huffington Post.

Calculating the answer is simpler than it seems: 19 people getting off the train can be represented by -19, and 17 people getting on the train as +17.

-19 + 17 = 2, meaning that there was a net loss of two people. If there are 63 people on the train now, that means there were 65 to begin with.

That said, many are convinced the answer is 46.

Here’s a full explanation of the answer.

## This question doesn’t actually involve math at all.

The Guardian pointed out the simple solution: turn the picture upside down and you’ll see that the numbers are in numerical order from 86 to 91.

## This word problem is a trick question.

Nothing is actually missing here — it’s just deliberately confusing wording. It all adds up if you look at the total, not the debt owed.

Twitter user Mat Whitehead laid it out in a table to show that there’s not a missing \$1 after all, which you can view here. ## This math question from Vietnam isn’t that difficult, but extremely time consuming.

The challenge: use each digit 1-9 only once to fill in the snake and make the equation equal 66 (colons are division signs).

According to VNEXPRESS, this puzzle is meant for third graders. There’s no trick or complicated math necessary — finding the correct configuration of numbers comes down to trial and error and process of elimination.

Here’s a tip: it’s easier if you rewrite the snake as an equation and follow the order of operations.

Here’s a full explanation of the answer from The Guardian.

# How to solve the maths puzzle for Vietnamese eight-year-olds that stumped parents and teachers

The challenge was to fill in the above snake with the digits 1 to 9, using each digit only once. The colon “:” means divide, and you must follow the standard order of operations, meaning that multiplication/division comes before addition/subtraction.

First, thanks to who all of you tried the problem and to those who wrote insightful and entertaining comments under the line. If you haven’t read the thread, it’s worth a read.

Now down to business. As I said when I set the question there is no complicated maths involved. We tame the Vietnamese snake by a process of trial and error, making educated guesses as we go.

Or, we write a simple computer program to solve it for us. Which is what many of you did. It is arguably a more instructive puzzle for budding computer scientists than it is for budding arithmeticians.

But for those of us who are old school pencil and paper folk:

Rewrite the snake as an equation:

a + (13b/c) + d + 12e – f – 11 + (gh/i)– 10 = 66

We are trying to find a, b, c, d, e, f, g, h and i, which we know are some combination of the digits 1,2,3,4,5,6,7,8 and 9.

Before we even look for a solution, consider the total number of ways we could fill in the snake: there are 362,880 possible combinations of the digits 1 to 9 placed in nine slots.

We can tidy the equation to:

a + (13b/c) + d + 12e – f +(gh/i) = 66 + 11 + 10 = 87

or

a + d – f + (13b/c) + 12e +(gh/i) = 87

From here we can assume that b/c and gh/i will be whole numbers, and also that we don’t want 13b/c to be too big.

Knowing this, we start plugging numbers in and seeing where we get to.

There is more than one solution, so there are many difference guesses that will lead to the right number. (I didn’t write a program, but many of you did and from the comments it would seem that there are well over 100 solutions.)

The most intuitive answer offered yesterday I thought belonged to the contributor Brollachain. To keep the term 13b/c as small as we can, he let b = 2 and c = 1.

Which gets us to

a + d – f + 26 + 12e +(gh/i) = 87

or

a + d – f + 12e +(gh/i) = 61

The numbers remaining are the digits from 3 to 9. They include the prime numbers 3, 5 and 7. As Brollachain recommends, lets get rid of them asap so they don’t complicate the other terms.

Let a = 3, d = 5 and f = 7.

Which leaves us with

3 + 5 – 7 + 12e +(gh/i) = 61

or

12e +(gh/i) = 60

The numbers remaining are 4,6,8,9.

Playing around with these gets us

e = 4

g = 9

h = 8

i = 6

48 + (72/6) = 48 +12 = 60

There are some puzzles that you solve with a flash of insight, and some others – like this one – where there is no alternative but trial and error.

Both kinds can be very satisfying to solve.

## More than 50% of students at Harvard, MIT, and Princeton got this question wrong.

It seems obvious that the answer is 10 cents, right? Wrong!

One dollar is only 90 cents more than 10 cents, not a full dollar more. The correct answer is five cents: \$0.05 + \$1.05 = \$1.10.

Here’s a full explanation of the answer.

# A simple logic question that most Harvard students get wrong

Harvard students get near-perfect SAT scores. These are smart, smart kids. So they shouldn’t have trouble with a simple logic question, right?

Try the following puzzle:

A bat and ball cost \$1.10.

The bat costs one dollar more than the ball.

How much does the ball cost?

Scroll down for the answer …

Behavioral economist Daniel Kahneman explains why most people get this wrong:

A number came to your mind. The number, of course, is 10: 10¢. The distinctive mark of this easy puzzle is that it evokes an answer that is intuitive, appealing, and wrong. Do the math, and you will see. If the ball costs 10¢, then the total cost will be \$1.20 (10¢ for the ball and \$1.10 for the bat), not \$1.10. The correct answer is 5¢. It is safe to assume that the intuitive answer also came to the mind of those who ended up with the correct number—they somehow managed to resist the intuition.

Many thousands of university students have answered the bat-and-ball puzzle, and the results are shocking. More than 50% of students at Harvard, MIT, and Princeton gave the intuitive—incorrect—answer. At less selective universities, the rate of demonstrable failure to check was in excess of 80%. The bat-and-ball problem is our first encounter with an observation that will be a recurrent theme of this book: many people are overconfident, prone to place too much faith in their intuitions. They apparently find cognitive effort at least mildly unpleasant and avoid it as much as possible.

This excerpt comes from Kahneman’s 2011 book, “Thinking, Fast And Slow,” which posits that we have an intuitive mental system and a logical mental system, and we often use the wrong one at the wrong time.

## Allegedly, only one out of 10 people could ace his math quiz without a calculator.

No calculator? No problem. The easiest way to go about solving this without a calculator is to round the numbers up or down to multiples of five, estimate the answer, and choose the option closest to your estimate.

Here’s a full rundown on how to do it.

# Only one in 10 people can pass this basic math test without using a calculator — but there’s a simple trick to do it

• Playbuzz user Bruce Boyena recently created a basic math testinvolving simple addition, subtraction, multiplication, and division.
• However, you can’t use a calculator.
• “Only 1 in 10 people will be able to pass,” Boyena claimed on his quiz.
• His test has gone viral, and some people seem to be stumped.
• An easy trick is to round numbers to the nearest multiple of five, and estimate the answer.
• Then, just use the process of elimination to choose the option that’s closest to your estimate.
• Test your skills on the three examples below or head to Playbuzzto take the full test and see the solutions.

### Although this trick isn’t always foolproof, you can do the math quickly and easily in your head.

Depending on what numbers you round to, you may have to decide between two likely options.

### Take the full test to find out if you have what it takes and see the solutions at Playbuzz. Talia is a reporter at INSIDER. Her human interest, travel, and lifestyle stories have been syndicated by Thrillist, Travel + Leisure, The Independent, and MSN. Previously, she wrote for The New York Jewish Week and SciShow Space. She earned a degree in English with a concentration in Creative Writing from Barnard College of Columbia University.