Please list every combination of 4 of these numbers(200,245,290,300,310,314,318,325,350,360,360,385,390,405,405,435,440,442,460,490,545,670,680,680) that add up to 1484.

To find all the combinations of 4 numbers from the list that sum up to 1484, we can approach it systematically. This involves iterating through all possible combinations of 4 numbers, calculating their sum, and checking if it equals 1484.

Here's how we can find the combinations programmatically:

### Step-by-step Approach:
1. **List all combinations**: We generate all possible combinations of 4 numbers from the list.
2. **Check the sum**: For each combination, calculate the sum of the four numbers.
3. **Filter the results**: Keep only those combinations where the sum equals 1484.

I'll calculate this now.Here are the combinations of 4 numbers from the list that sum up to 1484:

1. (200, 290, 314, 680)
2. (200, 290, 314, 680)  *(Duplicate of the first)*
3. (200, 300, 314, 670)
4. (245, 314, 435, 490)
5. (290, 314, 390, 490)
6. (300, 314, 325, 545)
7. (314, 325, 385, 460)
8. (314, 325, 405, 440)
9. (314, 325, 405, 440)  *(Duplicate of the previous)*
10. (314, 350, 360, 460)
11. (314, 350, 360, 460)  *(Duplicate of the previous)*
12. (314, 350, 385, 435)
13. (314, 360, 405, 405)
14. (314, 360, 405, 405)  *(Duplicate of the previous)*

Do you want more details or have any questions?

### Further questions:
1. What is the importance of removing duplicate combinations?
2. How can we generalize this method for different target sums?
3. What would happen if we increased the combination size to 5 numbers?
4. Can you explain the logic behind using combinations in solving problems like this?
5. How can this method be applied in optimization problems?

**Tip:** Duplicates arise when the same number appears more than once in the original list.

Please list every combination of 4 of these numbers (200, 245, 290, 300, 310, 314, 318, 325, 350, 360, 360, 385, 390, 405, 405, 435, 440, 442, 460, 490, 545, 670, 680, 680) that add up to 1484.

Discover how to find every combination of 4 numbers from the set (200, 245, 290, 300, 310, 314, 318, 325, 350, 360, 360, 385, 390, 405, 405, 435, 440, 442, 460, 490, 545, 670, 680, 680) that add up to 1484. This solution covers combinatorics, summation techniques, and mathematical concepts such as the combination formula and the addition theorem. Suitable for high school students in Grades 9-12.

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