Why 90% of People Fail This Deceptively Simple Math Puzzle (And How to Solve It)

The internet is universally captivated by brain teasers, optical illusions, and cognitive challenges. Yet, nothing quite sparks a fiery debate like a seemingly elementary math problem that somehow manages to confound the vast majority of people who attempt it. A specific arithmetic puzzle has recently resurfaced, boasting a staggering 90% failure rate, and it goes a little something like this:

3 + 3 × 3 − 3 + 3 = ?

At first glance, the sequence appears almost juvenile—a string of single-digit numbers and basic arithmetic symbols that most adults would expect to breeze through. However, the trap lies precisely in that overconfidence. If you blurted out “18” as your final answer, you have fallen into the very same snare that catches nine out of ten people.

So, why do so many intelligent individuals stumble on a problem they likely encountered in grade school? The answer lies in the human brain’s instinctive processing and a fundamental misunderstanding of mathematical hierarchy.

The Trap of Linear Thinking When presented with a sequence, the natural cognitive reflex is to process the information linearly from left to right, much like reading a sentence in a book. Applying this approach to the equation yields the following:

3 + 3 = 6 6 × 3 = 18 18 − 3 = 15 15 + 3 = 18

While this methodology feels intuitive, it entirely bypasses the foundational rules of mathematics. In arithmetic, not all operations are created equal, and performing them out of sequence fundamentally alters the outcome.

The Rule That Changes Everything: Order of Operations To arrive at the correct solution, one must employ the universally recognized mathematical rule known as the “Order of Operations.” Depending on where you went to school, you likely memorized this via an acronym—PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) or BODMAS (Brackets, Orders, Division, Multiplication, Addition, Subtraction).

These acronyms serve as a strict hierarchical map, dictating exactly how an equation must be deconstructed. According to these rules, multiplication and division must always be resolved before addition and subtraction, moving from left to right within each tier of hierarchy.

Applying the Order of Operations Let us apply the correct mathematical framework to our puzzle:

The original equation: 3 + 3 × 3 − 3 + 3 = ?

Step 1: Identify and resolve the multiplication. In this sequence, the only multiplication is 3 × 3, which equals 9.

Step 2: Substitute that result back into the original equation, effectively replacing the multiplication component with its product. The equation now reads:

3 + 9 − 3 + 3 = ?

Step 3: With multiplication out of the way, we are left solely with addition and subtraction. Because these operations share the same level of hierarchy, we now revert to our natural left-to-right processing.

3 + 9 = 12 12 − 3 = 9 9 + 3 = 12

The correct answer is unequivocally 12.

Why It Matters You might find yourself asking, “Why does this matter outside of a middle school math exam?” The reality is that the order of operations is far more than an arbitrary academic rule; it is the fundamental syntax of the universal language of mathematics. Without it, complex calculations in engineering, programming, economics, and physics would be entirely subjective and disastrously inconsistent.

When a programmer writes code or an architect calculates structural loads, there can be no ambiguity. The order of operations ensures that regardless of who is computing the equation, the result is identical.

Cognitive psychologists note that puzzles like this are incredibly valuable mental exercises. They force us to override our automatic, System 1 thinking—the fast, instinctive, and often error-prone part of our brain—and engage our deliberate, System 2 thinking, which requires effort and rule application.

The next time you encounter a string of numbers that looks too simple to take seriously, remember the 90% failure rate. Taking a moment to pause, recall the rules of mathematical hierarchy, and approach the problem methodically can be the difference between falling into a cognitive trap and emerging with the correct answer.