Interchange two numbers to make the equation correct: 18 × 3 ÷ 9 + 5 − 6 = 2

To make the given equation correct, we need to interchange two numbers.
The original equation is:

$$18 \times 3 \div 9 + 5 - 6 = 2$$

First, let's evaluate the Left Hand Side (LHS) of the original equation:

$$18 \times 3 \div 9 + 5 - 6$$ $$= 54 \div 9 + 5 - 6$$ $$= 6 + 5 - 6$$ $$= 11 - 6$$ $$= 5$$

Since $5 \neq 2$, the original equation is incorrect. We need to find which interchange makes it correct.

Let's test each option:

• Option 1: Interchange 18 and 6 The equation becomes:

  $$6 \times 3 \div 9 + 5 - 18 = 2$$

  Evaluate LHS:

  $$6 \times 3 \div 9 + 5 - 18$$ $$= 18 \div 9 + 5 - 18$$ $$= 2 + 5 - 18$$ $$= 7 - 18$$ $$= -11$$

  Since $-11 \neq 2$, this option is incorrect.

• Option 2: Interchange 3 and 5 The equation becomes:

  $$18 \times 5 \div 9 + 3 - 6 = 2$$

  Evaluate LHS:

  $$18 \times 5 \div 9 + 3 - 6$$ $$= 90 \div 9 + 3 - 6$$ $$= 10 + 3 - 6$$ $$= 13 - 6$$ $$= 7$$

  Since $7 \neq 2$, this option is incorrect.

• Option 3: Interchange 2 and 3 This means we replace '3' on the left side with '2', and '2' (the result on the right side) with '3'. The equation becomes:

  $$18 \times 2 \div 9 + 5 - 6 = 3$$

  Evaluate LHS:

  $$18 \times 2 \div 9 + 5 - 6$$ $$= 36 \div 9 + 5 - 6$$ $$= 4 + 5 - 6$$ $$= 9 - 6$$ $$= 3$$

  Since $3 = 3$, this equation is correct. This option works.

• Option 4: Interchange 5 and 9 The equation becomes:

  $$18 \times 3 \div 5 + 9 - 6 = 2$$

  Evaluate LHS:

  $$18 \times 3 \div 5 + 9 - 6$$ $$= 54 \div 5 + 9 - 6$$ $$= 10.8 + 9 - 6$$ $$= 19.8 - 6$$ $$= 13.8$$

  Since $13.8 \neq 2$, this option is incorrect.

Therefore, interchanging 2 and 3 makes the equation correct.

The final answer is $\text{3}$