11 – 11 × 11 + 11. At first glance, this calculation looks like a children’s riddle. But in reality, it seriously tests our mathematical logic, however firmly ingrained it may have been since school. This kind of puzzle is as captivating as it is baffling: because no, it’s not simply a matter of addition and subtraction… The key is to remember the order of operations. So, ready to take on the challenge without cheating? Come on, let’s use our brains, not our calculators!

 

 A Simple Calculation That Outsmarts Our Brain

At first glance, 11 – 11 × 11 + 11 looks like something you might find scribbled in the margin of a child’s math notebook. It’s short. It’s neat. It only uses one number. Surely, it can’t be that hard.

And yet, this tiny expression has a habit of stopping people in their tracks.

Ask a room full of students, adults, or even professionals to solve it quickly, and you’ll get a surprising range of answers. Some will say 121. Others might say 0. A few will pause, frown, and ask for clarification. Very few will immediately give the correct result with confidence.

Why?

Because this isn’t really a test of arithmetic.
It’s a test of how well we remember — and apply — the order of operations.

This is where math stops being about numbers and starts being about logic, habits, and the shortcuts our brains love to take.

So let’s slow down, put calculators away, and unpack why this “simple” problem is such a powerful mental trap.

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Why Simple Math Can Be So Tricky

Humans are excellent pattern-recognition machines. We’re wired to look at something familiar and jump to a conclusion as fast as possible. That’s usually a good thing — it helps us read quickly, react quickly, and make decisions without overthinking every detail.

But in math, this instinct can work against us.

When we see a sequence like:

11 – 11 × 11 + 11

our brain often reads it the way we read text: from left to right.

So we instinctively want to do:

• 11 – 11 = 0

• 0 × 11 = 0

• 0 + 11 = 11

It feels logical. It feels natural. And it’s completely wrong.

Not because the arithmetic is wrong — but because the approach is.

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The Forgotten Rule That Changes Everything

Most of us were taught the order of operations in school. Depending on where you grew up, you might remember it as:

• PEMDAS
  (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction)

or

• BODMAS / BIDMAS
  (Brackets, Orders, Division and Multiplication, Addition and Subtraction)

Different names, same idea.

The key principle is this:

Multiplication and division come before addition and subtraction.

And just as importantly:

Addition and subtraction are performed from left to right — but only after multiplication and division are done.

This rule isn’t arbitrary. It exists so that mathematical expressions have one clear, universal meaning. Without it, math would be chaos.

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Applying the Rule Step by Step

Let’s return to our expression:

11 – 11 × 11 + 11

Step 1: Identify Multiplication

There is only one multiplication here:

11 × 11

According to the order of operations, this must be done before any addition or subtraction.

Step 2: Do the Multiplication

11 × 11 = 121

Now rewrite the expression:

11 – 121 + 11

Step 3: Handle Addition and Subtraction (Left to Right)

Now that only addition and subtraction remain, we move left to right.

• 11 – 121 = –110

• –110 + 11 = –99

✅ Final Answer: –99

That’s it.

No tricks. No hidden meanings. Just the rules — applied correctly.

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Why So Many People Get It Wrong

If the rules are so clear, why do so many people stumble?

1. Left-to-Right Bias

We’re taught to read from left to right, so we subconsciously apply that habit to math — even when it doesn’t apply.

2. Overconfidence with Simple Numbers

Because all the numbers are the same (11), the expression feels harmless. Our brain thinks, “I’ve got this,” and stops checking the rules.

3. Fading Math Foundations

Many adults haven’t actively used formal math rules in years. The knowledge is still there, but it’s dusty — and under pressure, habits replace rules.

4. Social Media Math Traps

These kinds of expressions often appear online as “gotcha” puzzles, designed to spark arguments. The speed of scrolling encourages fast answers, not careful thinking.

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This Isn’t Just About Math

What makes this puzzle fascinating is that it reveals something deeper than numerical skill.

It shows us how:

• We rely on intuition even when rules matter

• We confuse familiarity with correctness

• We underestimate “simple” problems

In that sense, 11 – 11 × 11 + 11 is less of a math problem and more of a thinking problem.

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A Brief History of the Order of Operations

The order of operations wasn’t always universally agreed upon. Early mathematics relied heavily on context and written explanations. As algebra developed, mathematicians needed a standardized system so expressions could be written compactly and understood the same way everywhere.

By the 19th century, the modern convention had become widely accepted. It allowed increasingly complex ideas to be expressed clearly — from physics equations to computer programming.

Without it, something as simple as:

3 + 5 × 2

could mean either 16 or 13, depending on interpretation.

Rules remove ambiguity. That’s their power.

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Why Calculators Don’t Save Us

Many people assume calculators will “fix” these problems. But calculators don’t think — they follow the same rules.

If you type:

11 – 11 × 11 + 11

into a standard calculator, it will give –99, because it applies the order of operations correctly.

The calculator isn’t smarter than us.
It’s just more disciplined.

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Training Your Brain to Slow Down

The real lesson here isn’t “remember PEMDAS.” It’s learning to pause.

Before solving any expression:

1. Scan for multiplication or division

2. Simplify those first

3. Then move left to right

Even a two-second pause can prevent most mistakes.

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Why These Puzzles Are So Popular

People love puzzles like this because they:

• Create surprise

• Challenge confidence

• Spark discussion

• Feel accessible to everyone

They remind us that learning isn’t about memorizing answers — it’s about understanding rules and knowing when to apply them.

And there’s something oddly satisfying about realizing why your first instinct was wrong.

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A Final Thought

So, is 11 – 11 × 11 + 11 a children’s riddle?

Not really.

Children who’ve recently learned the order of operations often get it right more easily than adults — because the rules are still fresh, and habits haven’t taken over yet.

In that way, this puzzle is a quiet reminder:

Clear thinking beats quick thinking.

And sometimes, the smallest problems are the best tests of how we think.

So next time you see a “simple” calculation, don’t rush.
Your brain is powerful — but only if you use it carefully. 🧠✨