Puzzles are often devised as a form of entertainment but they can also arise from serious mathematical or logistical problems. In such cases, their solution may be a significant contribution to mathematical research.
Recently, a puzzle is going viral on the Internet which is confusing everyone’s minds.
What is 6÷2(1+2) =?
This bizarre puzzle asks you to solve the equation and it has two answers. The problem often generates debate and has millions of comments on Facebook, Twitter, YouTube and other social media sites.
If you end up with an answer of either 1 or 9, you’re RIGHT !.
The vast majority of people ended up with either one of those answers. Some reportedly think it is 0, 3, or even 6, but none of those three answers are at all correct.
However, the reason why 9 and 1 are given as the main answers for this problem all boils down to how people were taught to do the math. Eventually, it led to numerous heated debate online. According to a report, only one out in a 1,000 people can figure out the second answer.
For an explanation of why the answers to this math problem vary,
Watch this video:
Here Is The Correct Answer Explained
The order of operations
The expression can be simplified by the order of operations, often remembered by the acronyms PEMDAS/BODMAS.
First, evaluate Parentheses/Brackets, then evaluate Exponents/Orders, then evaluate Multiplication-Division, and finally evaluate Addition-Subtraction.
Everyone is in agreement about the first step: simplify the addition inside of the parentheses.
6÷2(1+2)
= 6÷2(3)
This is where the debate starts.
The answer is 9
If you type 6÷2(3) into a calculator, Google or WolframAlpha, the input has to be parsed and then computed. All of these will first convert the parentheses into an implied multiplication. The expression becomes the following.
6÷2(3)
= 6÷2×3
According to the order of operations, division and multiplication have the same precedence, so the correct order is to evaluate from left to right. First take 6 and divide it by 2, and then multiply by 3.
6÷2×3
= 3×3
= 9
This gets to the correct answer of 9.
Some people have a different interpretation. And while it’s not the correct answer today, it would have been regarded as the correct answer 100 years ago.
The other result of 1
Historically the symbol ÷ was used to mean you should divide by the entire product on the right of the symbol (see longer explanation below).
Under that interpretation:
6÷2(3)
= 6÷(2(3))
(Important: this is outdated usage!)
From this stage, the rest of the calculation works by the order of operations. First we evaluate the multiplication inside the parentheses. So we multiply 2 by 3 to get 6. And then we divide 6 by 6.
6÷(2(3))
= 6÷6
= 1
This gives the result of 1. This is not the correct answer; rather it is what someone might have interpreted the expression according to old usage.