This viral math problem has generated an extraordinary amount of controversy because of an obscure yet perfectly valid point that you might not have heard of. Can you figure out what that highly contentious issue might be?
If you’re somewhat familiar with online math brainteasers like this one, it’s clear that this problem deals with what’s known as the “order of operations.” The acronym for remembering this is PEMDAS/BODMAS, which breaks down as follows:
And as a rule, any expression of the same precedence is dealt with from left to right.
Literally millions of people online have tried this math problem on various social media platforms, and it has sparked a massive debate over what the correct answer is. Despite how clearly the order of operations are understood in the community of mathematics, the debate has split netizens into two main camps, which we shall explore here.
So, go ahead and solve the viral math problem, shown below, for yourself before scrolling down to find out what all of the fuss is about. What answer did you get? And which of the two camps do you belong to?
When you’ve found the solution, scroll down to see what others have come up with online.
Seems pretty straightforward, right? Well, it’s not quite as simple as you may have thought.
Following the order of operations, the first precedent to be dealt with is the parenthetical expression (9 + 3), which is (12).
Next, we are left with the expression 48 ÷ 2(12). The parenthetical expression 2(12) is implicitly one of multiplication: 2 x 12. Then, if we follow the standard, modern order of operations as per above, multiplication and division are of the same precedent, and so, they are dealt, as per our rule, from left to right.
Also, that is exactly how any calculator would interpret such an expression—using the same order of operations as mentioned.
Thus, 48 ÷ 2 gives us 24, which is multiplied by 12, which gives us a final answer of 288. Was this your answer? Then that might seem like the end of the story, but it’s not, and here’s why:
Dating back to an earlier age, there is an obscure exception to the modern rules for the order of operations from 1917 that was once in use. According to this exception, parenthetical expressions that are implicitly multiplication, like 2(12), are not treated in the same way as 2 x 12 would be, as per the order of operations.
Rather, the expression would 2(12) takes precedent over that of division and multiplication; it would be grouped in the same way the expression 2y would be, for instance. And the reason for this was one of expediency, as it would be simpler and easier to denote 48 ÷ 2(12) as such than it would be to denote the cumbersome expression:. Such an exception was thus applied.
Thus, going by the old the rule from 1917…
The parenthetical expression 2(12) is not implicitly dealt with like multiplication and division, and instead takes precedent. So, 2(12) equals 24, and 48 ÷ 24 gives us our final answer: 2.
Depending on which rule is used, there are two completely different answers. Most modern schools teach the first method, the one that our calculators follow, but there are some people out there who continue to follow the ways of olden times.
Which camp do you belong to?
BONUS: Are you up for an even bigger challenge? Try this one on for size!
Here’s Another Controversial Math Problem–and People Are Getting Into Heated Arguments Over It
This math problem was originally created for 5-year-olds in China. It might seem simple enough at first; however, a fierce debate ensued when the question first appeared online—and that’s what makes it so interesting.
First, see if you can figure out the answer for yourself, and then we’ll dig into what all the clamor is about.
Note that there are pictorial differences between the flowers; the 2 yellow flowers in the third row are not equal to the single yellow flower in the last row. Also note that the number of blue petals on each of the blue flowers are not all the same.
Solve the problem in the illustration below:
Do not scroll down right away! Take a moment or two to come up with the solution, and then, when you’re ready (or if you’re completely stumped), check down below to see the answer and find out which side of the debate you ended up siding with.
Most people agreed that the correct solution is 81
Now here’s an explanation of how this was arrived at, as well as what all the the trivia surrounding this problem was about:
In the first line, there are 3 red flowers added together to equal 60. That means that each red flower is equal to 20.
In the second line, we can assign that value of 20 for the red flower, and adding 2 blue flowers (with 5 petals each) gives us 30. We can subtract 20 on both sides of the equation, which leaves us with 2 blue flowers (with 5 petals each) equaling 10. That means that 1 blue flower (with 5 petals) equals 5.
In the third line, we can plug in the value of 5 for the single blue flower (with 5 petals), and subtracting 2 yellow flowers gives us 3. In this equation, 2 yellow flowers equal 2, which means that 1 yellow flower equals 1.
In the final equation, we can assign a value of 1 for the single yellow flower and 20 for the red flower—however, what number is to be assigned to the blue flower with only 4 petals? Some of the debate swirled around precisely that matter.
Arguably, the value of the 4-petaled flower remains unknown without any more information to tell us that, meaning that the solution is unsolvable.
However, the consensus was that while the value of a 5-petaled blue flower is 5, the value of a 4-petaled blue flower is 4, or in other words, the value of each blue flower petal is 1, and thus, the value of the 4-petaled blue flower is 4.
Plugging in this information into the equation, we simply multiply 20 by 4 and add 1 to get a final answer of 81.
This answer appears to be what the problem’s creators had in mind whether we like it or not!
This solution can be considered problematic if you wish to get finicky. For example, the blue flower also has a stem, a leaf, and a center, all of which arguably could be assigned a value that is impossible to determine.
And you can get even more finicky if you want to dig into other pictorial trivia, as some netizens who love nothing more than to argue endlessly surely will.
What answer did you get, and what do you think of the debate surrounding this whole controversy?
Photo Credit: The Epoch Times