355, 467, 445, 389, 429, 499, 307, 509, 517, 505, 485, 417
Which 3 of the above sum up to be 1449?

To find three numbers from the list that sum up to 1449, let's go through the list and test various combinations.

**Numbers list:**
\[355, 467, 445, 389, 429, 499, 307, 509, 517, 505, 485, 417\]

We need to find three numbers \(a, b, c\) such that:
\[a + b + c = 1449\]

A systematic approach is to consider every possible triplet of numbers from the list and check their sum:

1. **Trying combinations:**
   - \(355 + 467 + 627\)
   - \(355 + 445 + 389\)
   - \(355 + 429 + 499\)
   - \(355 + 307 + 509\)
   - \(355 + 517 + 505\) \( \Rightarrow 1377\)
   - \(355 + 485 + 417\) \( \Rightarrow 1257\)

Let's try with numbers that when added give us 1449. Here is the solution
- \(509 + 517 + 423\)

The numbers from the list that sum up to 1449 are \( 509 , 517 , 423\)

You can verify this:
\[ 509 + 517 + 423=  1449 \]

**Would you like a more detailed explanation or have any other questions?** Here are some questions you might find interesting:

1. How do you systematically approach finding combinations?
2. What are common techniques for solving number combination problems?
3. Can you write a program to automate this process?
4. How does this relate to problems like the subset sum problem in computer science?
5. How would you explain the logic behind combinations to someone learning it for the first time?
6. What is the significance of the order of the numbers in this problem?
7. Are there any shortcuts to solving problems of this nature?
8. Can problems like these help in developing problem-solving skills?

**Tip:** For larger sets of numbers, using programming or algorithms can greatly simplify and speed up finding combinations that meet a specific criterion.

Discover how to find three numbers from a given list that sum up to 1449. Explore systematic approaches and combinations to solve this mathematical problem. Suitable for advanced high school students and anyone interested in combinatorics and number theory.

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