Explanation:

- To check which numbers need to be interchanged, we evaluate the equation: $10\times 18+216÷5-41=21.$

- Calculate parts separately:

- $10\times 18=180.$

- $216÷5=43.2.$

- Overall operation becomes $180+43.2-41.$

- Simplify: $180+43.2=223.2.$

- Subtract 41: $223.2-41=182.2.$

- Clearly, 182.2 does not equal 21. Must swap numbers to fix this.

- Option 1: Interchanging 216 and 18 doesn't work as recalculations don't equal 21.

- Option 2: Interchanging 10 and 41 doesn't work either.

- Option 3: Interchanging 5 and 10 doesn't yield 21.

- Option 4: Interchanging 18 and 5 makes it: $10\times 5+216÷18-41.$

- $10\times 5=50.$

- $216÷18=12.$

- Simplify: $50+12=62.$

- Subtract 41: $62-41=21.$