Math Challenge: The Puzzle Everyone Debates
A popular image-based brain teaser asks a seemingly simple question:
11 − 11 × 11 + 11 = ?
It’s designed to test whether you follow the standard rules of arithmetic, especially order of operations.
What Makes This Problem Tricky
Many people try to solve the expression from left to right. That approach often leads to the wrong result because multiplication must be handled before addition and subtraction.
Key idea:
- Multiplication comes before addition/subtraction in standard math rules.
The Rule You Must Use: Order of Operations
To solve correctly, apply the common rule set (often remembered as PEMDAS/BODMAS):
- Parentheses/Brackets (none here)
- Exponents/Orders (none here)
- Multiplication and Division (left to right)
- Addition and Subtraction (left to right)
Step-by-Step Solution (Easy Breakdown)
Expression: 11 − 11 × 11 + 11
- Compute the multiplication first:
- 11 × 11 = 121
- Substitute back into the expression:
- 11 − 121 + 11
- Now do subtraction/addition from left to right:
- 11 − 121 = −110
- −110 + 11 = −99
Final Answer
- 11 − 11 × 11 + 11 = −99
Common Wrong Answer (And Why It Happens)
A frequent mistake is solving left to right:
- (11 − 11) × 11 + 11 = 0 × 11 + 11 = 11
This is incorrect because it changes the structure of the original expression by treating subtraction as if it must happen before multiplication.
Why These Puzzles Go Viral
These challenges spread quickly because they:
- Look simple at first glance
- Expose a common mistake about operation priority
- Spark debate between “left-to-right” thinking and formal arithmetic rules
