Number Logic Puzzle: Identifying the Outlier

This problem asks us to identify which number among the given options does not share a common characteristic with the others. This type of question tests our ability to recognize patterns and logical connections between numerical values.

Analyzing the Options

Let's examine each number provided in the options:

• Option 1: $123$
• Option 2: $213$
• Option 3: $212$
• Option 4: $312$

Finding the Underlying Pattern

To find the number that does not belong, we can investigate the properties of the digits within each number:

• The number $123$ is composed of the digits $1$, $2$, and $3$. All these digits are distinct (unique).
• The number $213$ is composed of the digits $2$, $1$, and $3$. All these digits are also distinct.
• The number $212$ is composed of the digits $2$, $1$, and $2$. Notice that the digit $2$ appears twice; it is a repeated digit.
• The number $312$ is composed of the digits $3$, $1$, and $2$. All these digits are distinct.

From this analysis, we can see a clear distinction. The numbers $123$, $213$, and $312$ are all formed using three unique digits. In contrast, the number $212$ uses the digit $2$ more than once.

Conclusion: The Number That Does Not Belong

The defining characteristic that separates the numbers is the uniqueness of their digits. Since $123$, $213$, and $312$ all contain unique digits, while $212$ contains a repeated digit, $212$ is the number that does not belong to the group.