`17-[18-{16-(5-bar(4-1))]=`?

Options

A. `25`
B. 13
C. 23
D. none of these

Answer

To solve the expression \( 17 - [18 - \{16 - (5 - |4 - 1|)\}] \), we will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often abbreviated as PEMDAS.

### Step-by-Step Solution:

1. **Calculate the innermost absolute value**:
\[ |4 - 1| = |3| = 3 \]
Now the expression becomes:
\[ 17 - [18 - \{16 - (5 - 3)\}] \]

2. **Simplify inside the parentheses**:
\[ 5 - 3 = 2 \]
Now the expression becomes:
\[ 17 - [18 - \{16 - 2\}] \]

3. **Simplify inside the curly brackets**:
\[ 16 - 2 = 14 \]
Now the expression becomes:
\[ 17 - [18 - 14] \]

4. **Simplify inside the square brackets**:
\[ 18 - 14 = 4 \]
Now the expression becomes:
\[ 17 - 4 \]

5. **Final subtraction**:
\[ 17 - 4 = 13 \]

Thus, the final answer is:
\[ \boxed{13} \]