There are plenty of ways to keep your brain active and engaged during the current lockdown, and a math challenge like this is one of them. Whether you’re already a math whiz or have let your mental arithmetic fall by the wayside since school, this is a puzzle you will surely find entertaining.
This equation, originally shared on Fun With Puzzles, will take you back to middle school math class with its seemingly simple components. But there’s a trick hiding beneath the surface of this equation; can you figure it out?
Have you seen a math puzzle like this before? Do you know how to solve it? To aid you, the puzzle offers four multiple-choice answers:
Take a moment to figure it out, and when you think you have your answer, or if you’re completely stumped, check down below for the solution.
The answer is: B. 25
Were you able to solve it? If so, then congratulations! If not, and if you are puzzled by this answer, see below for an explanation. This was a tricky one even for the best of us!
Firstly, this problem involves a mathematical convention known as the “order of operations,” but it adds a bit of a twist that might catch some of us off guard, as we shall explain.
The order of operations is a rule that tells us which functions should be solved in what order. There is a handy acronym for remembering this rule: PEMDAS. That is, the problem should be solved in the following order: Parentheses first, Exponents next, then Multiplication and Division (which are interchangeable at this stage), and Addition and Subtraction (also interchangeable) last of all.
Functions that are interchangeable at a certain stage in solving the problem should be solved in the order from left to right.
So, let’s look at our original question once again and solve it using this method:
5 x 5 ÷ 5 (1 + 4) = ?
First, we solve the parentheses: (1 + 4) = 5. Thus: 5 × 5 ÷ 5 (5) = ?
There are no exponents, so the next stage is multiplication and division from left to right. Now, here is the “trick” where some people might have been caught off guard. Some might have proceeded to solve 5(5) at this stage, as some conventions of math specify to do where there are parentheses—in which case you would have ended up with a final answer of A. 1 and may be forgiven or even granted a pass, perhaps.
Yet, for the sake of consistency, we shall solve this according to the standardized approach using PEMDAS.
So, solving multiplication and division from left to right, we proceed to solve it thus: 5 × 5 = 25; then division: 25 ÷ 5 = 5, and lastly: 5(5) = 25.
The final answer is B. 25
If you got the answer, then we want to congratulate you for sidestepping this little twist in the order of operations, as it could easily have slipped a keen observer’s notice. Or if you assert that this unconventional little trick should be disqualified and the answer should be something different, more power to you!
According to The Math Forum, the consensus for the order of operations was reached among mathematicians many years ago as a way to universalize the way we approach equations; if the rules are adhered to, every individual is able to achieve the same solution to any given problem.
In any case, if this puzzle provided some level of mental stimulation during these dreary days at home, it will have served its purpose! Please feel free to share it with someone you know who is in need of some mental activity!