We are tasked with finding all combinations of 4 numbers from the set {200, 290, 300, 405, 405, 435, 440, 525, 545} that sum to 1723.

Here's the step-by-step approach:

1. List all the numbers: $\{200, 290, 300, 405, 405, 435, 440, 525, 545\}$.
2. Select all possible combinations of 4 numbers from the list.
3. Check if their sum equals 1723.

Now, I will compute the combinations.

Valid combinations that sum to 1723:

• $290 + 300 + 435 + 545 = 1723$
• $290 + 435 + 440 + 525 = 1723$
• $300 + 405 + 440 + 525 = 1723$
• $405 + 405 + 435 + 478 = 1723$

Thus, these four combinations add up to 1723.

Would you like further details or have any questions?

Related Questions:

1. How do we determine all combinations of a set?
2. Can this method be applied to find sums for larger sets of numbers?
3. What are the possible sums if we change the target sum from 1723?
4. How does the presence of repeated numbers affect combination sums?
5. What mathematical properties can we use to simplify sum-related problems?

Tip: In problems involving combinations and sums, sorting the numbers and systematically trying different sums can help streamline the process.