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Can You Solve This “Only Genius” Math Puzzle? The Answer May Be Simpler Than You Think
At first glance, the equation in the image looks incredibly simple:
5 × 5 − 5 + 5 ÷ 5 = ?
There are only four numbers and three basic mathematical operations.
No complicated fractions.
No square roots.
No algebra.
No hidden variables.
Yet this kind of puzzle can still make people stop and think.
The image even adds the playful challenge:
“Only Genius”
So, what is the correct answer?
Is it 21?
Or could there be another interpretation?
Let’s break it down carefully.
The First Thing You Need to Know: Order of Operations
The key to solving this puzzle is understanding the order of operations.
When an expression contains multiplication, division, addition, and subtraction, you cannot simply calculate everything from left to right.
Instead, multiplication and division are performed before addition and subtraction.
A commonly used mnemonic is PEMDAS:
P = Parentheses
E = Exponents
M = Multiplication
D = Division
A = Addition
S = Subtraction
Another way to remember it is:
Parentheses → Exponents → Multiplication/Division → Addition/Subtraction
The important detail is that multiplication and division have the same priority, while addition and subtraction also have the same priority.
When operations have equal priority, you work from left to right.
This rule is what determines the answer to the puzzle.
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Step 1: Look at the Multiplication
The expression is:
5 × 5 − 5 + 5 ÷ 5
The first multiplication is:
5 × 5 = 25
So now the expression becomes:
25 − 5 + 5 ÷ 5
But we’re not finished.
There is still a division operation.
Step 2: Calculate the Division
Next:
5 ÷ 5 = 1
Now the equation becomes:
25 − 5 + 1
At this point, there is no multiplication or division left.
So we move on to subtraction and addition.
Step 3: Work From Left to Right
Now we have:
25 − 5 + 1
Because subtraction and addition have equal priority, we solve from left to right.
First:
25 − 5 = 20
Then:
20 + 1 = 21
Therefore:
5 × 5 − 5 + 5 ÷ 5 = 21
So the correct answer is:
21
Why Do Some People Get a Different Answer?
This is where the puzzle becomes interesting.
Some people see:
5 × 5 − 5 + 5 ÷ 5
and immediately start calculating from left to right:
5 × 5 = 25
25 − 5 = 20
20 + 5 = 25
25 ÷ 5 = 5
They might therefore answer:
5
But that’s incorrect under the standard order of operations.
The mistake is performing the division at the end.
The expression contains:
5 + 5 ÷ 5
The division must happen before the addition.
So:
5 + 5 ÷ 5
becomes:
5 + 1
which equals:
6
It does not become:
10 ÷ 5 = 2
And the entire equation therefore doesn’t equal 5.
What If You Simply Calculate From Left to Right?
Let’s compare the two approaches.
Incorrect approach:
5 × 5 − 5 + 5 ÷ 5
Calculate everything from left to right:
25 − 5 + 5 ÷ 5
20 + 5 ÷ 5
25 ÷ 5
= 5
The problem is that this ignores the standard priority of multiplication and division.
Correct approach:
5 × 5 − 5 + 5 ÷ 5
First multiplication:
25 − 5 + 5 ÷ 5
Then division:
25 − 5 + 1
Then left-to-right addition/subtraction:
20 + 1
= 21
That’s why the correct answer is 21.
The Interesting Part: Multiplication and Division Are Equal
There’s another common misconception about order of operations.
Some people memorize PEMDAS and interpret it as:
Multiplication always comes before division.
That’s not quite right.
Multiplication and division have the same level of precedence.
Similarly, addition and subtraction have the same level of precedence.
For example:
20 ÷ 5 × 2
You don’t automatically multiply first.
You work from left to right: