Viral Maths Problems

Every year, we see a fresh wave of 'viral' maths problems. You know the ones: 'Can you solve this?' The catch is, they rarely give you the answer, and the equations are usually a mess. Let's unpack one of these problems to see why they’re so confusing—and how we can actually fix them.


Example

The last one I saw online was the challenge:
Can you solve?
8 ÷ 2(2+2)
My first observation is the unusual use of ÷ (mathematicians prefer /) and bad bracketing.

Let us clean up the expression to clear up some ambiguity:
8 ÷ 2 × (2+2)
This makes it much easier to the next step of applying BODMAS (US refers to this as PEDMAS) .
The order of operations here are:
  1. Solve the Brackets, then
  2. From left to right apply division's and multiplications
  3. From left to right apply addition's and subtraction's
Here: division and multiplication have equal precedence as do addition and subtraction.
Applying these operations gives:

8 ÷ 2(2+2) = 8 ÷ 2 × (2 + 2)
                 =  8 ÷ 2 × 4
                 =  4 × 4
                 =  16
So, why is this a badly formed question? A goal of mathematics is to accurately and unambiguously provide solutions to problems. The real challenge is to answer the right problem. If the purpose of the problem was to provide a correct answer and not lead to argument on interpretation then the question could have been asked in a number of different ways:

Question

What is (8 ÷ 2) × (2 + 2) ?

Answer

(8 ÷ 2) × (2 + 2) = (4) × (4) = 4 × 4 = 16
Or, you could ask:

Question

What is 8 ÷ (2 × (2 + 2)) ?

Answer

8 ÷ (2 × (2 + 2)) = 8 ÷ (2 × 4) = 8 ÷ 8 = 1
Another variant of this question could be:

Question

Explain the order of operations for 8 ÷ 2 × (2 + 2)  ?

Answer

Apply BODMAS and evaluate from left to right:
  1. First evaluate the terms inside the brackets:
    8 ÷ 2 × (2 + 2) = 8 ÷ 2 × 4
  2. Then evaluation from left to right:
    8 ÷ 2 × 4 = 4 × 4
  3. Giving the final operation:
    4 × 4 = 16
So, the problem could be much clearer about it's intent.
What was the point of the original challenge?
I feel that the problem as stated in so many online forums is more click-bait to generate an argument than as a pedagogical exercise.

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