Step-by-step Solution:

Quick Solution

This puzzle requires us to first substitute the mathematical operators with their new meanings and then solve the resulting expression using the standard order of operations (BODMAS/PEMDAS).

1. Substitute the Operators

The given substitutions are:

• ÷ becomes + (addition)
• - becomes ÷ (division)
• × becomes - (subtraction)
• + becomes × (multiplication)

The original expression is: (36 × 4) - 8 × 4 / (4 + 8 × 2 + 16 ÷ 1)

Applying the substitutions, the new expression becomes:

 (36 - 4) ÷ 8 - 4 
4 × 8 - 2 × 16 + 1

2. Evaluate the New Expression

We solve the numerator and the denominator separately, following the order of operations.

• Numerator Calculation:(36 - 4) ÷ 8 - 4
= 32 ÷ 8 - 4
= 4 - 4
= 0
• Denominator Calculation:4 × 8 - 2 × 16 + 1
= 32 - 32 + 1
= 0 + 1
= 1

3. Final Calculation

Now we divide the value of the numerator by the value of the denominator:

Result = 0 / 1 = 0

Final Answer: The value of the expression is 0.