You can make numbers 0 through 5 by using the numbers 1, 2, and 4 exactly once in each case, combining them with basic arithmetic operations like addition and subtraction. Here's how to achieve each number:

1. 0: $4 - 2 - 1 = 0$
2. 1: $4 - 2 + 1 = 1$
3. 2: $4 - 2 = 2$
4. 3: $4 + 1 - 2 = 3$
5. 4: $4 + 1 - (2 - 1) = 4$
6. 5: $4 + 2 - 1 = 5$

Would you like to explore further details on these calculations or ask about a similar puzzle? Here are some related questions:

1. Can you make higher numbers using only 1, 2, and 4?
2. What is the role of multiplication in such puzzles?
3. How would the puzzle change if more operations were allowed?
4. How could you make negative numbers using the same set?
5. Can you construct 6 using other methods with the same numbers?

Tip: Always explore the full range of basic arithmetic operations when solving number puzzles like this!