Step 1: Read the pattern.
We are told 841 gives 3, 633 gives 5, and 425 gives 7. We must find what 217 gives.
Step 2: Look at the three digits.
Take the first digit, the second digit, and the third digit of each number and try a simple rule.
Step 3: Test a rule on 841.
Divide the first by the second, then add the third. So $8 \div 4 + 1 = 2 + 1 = 3$, which matches.
Step 4: Check it on the others.
For 633, $6 \div 3 + 3 = 2 + 3 = 5$, correct. For 425, $4 \div 2 + 5 = 2 + 5 = 7$, also correct.
Step 5: Apply to 217.
Now do $2 \div 1 + 7 = 2 + 7 = 9$.
Step 6: Conclusion.
So 217 gives \[ \boxed{9} \]