To make the number 3 using the numbers 5, 4, 9, and 1, and ensuring that each number is used exactly once, we can use the following expression:

$\frac{9 - 4 + 1}{5} = \frac{6}{5} = 1.2$

This expression does not yield 3 exactly, so let's reconsider the approach.

Unfortunately, there isn't a straightforward way to exactly achieve the number 3 using basic arithmetic operations (addition, subtraction, multiplication, division) and using the numbers 5, 4, 9, and 1 exactly once. You might need to use more advanced operations or different interpretations of the numbers to achieve the desired result. However, these operations go beyond basic arithmetic.

Would you like to explore more complex operations or alternate interpretations?

Here are five related questions:

1. Can you make the number 7 using these numbers?
2. Can you achieve 3 by using any two of the numbers provided?
3. What other target numbers can be made using these numbers exactly once?
4. How can factorials or exponents be used with these numbers to reach a specific target?
5. What happens if you allow concatenation of the numbers (e.g., using "41" or "95")?

Tip: Experimenting with different operations like square roots, powers, or factorials can sometimes help reach a solution for tricky number puzzles.