To solve this problem, we need to identify all possible combinations of four numbers from the list provided that sum up to 1629.

The list of numbers is:

$200, 245, 290, 300, 310, 314, 318, 325, 360, 360, 385, 390, 405, 405, 435, 440, 442, 460, 490, 495, 545, 670, 680, 680$

I'll go ahead and compute this systematically to find every valid combination.Here are all the combinations of four numbers from the provided list that sum up to 1629:

1. (200, 314, 435, 680)
2. (245, 314, 390, 680)
3. (310, 314, 325, 680)
4. (310, 314, 460, 545)
5. (314, 360, 460, 495)
6. (314, 385, 435, 495)
7. (314, 385, 440, 490)
8. (314, 390, 435, 490)

Some combinations appear twice due to the repetition of numbers in the original list.

Would you like more details about how these combinations were found or have any further questions?

Here are 5 related questions:

1. How would the solution change if there were only unique numbers?
2. Can you find the combinations for a different target sum?
3. What happens if we increase the number of numbers selected to 5?
4. How does repetition of numbers affect the number of valid combinations?
5. What other methods can be used to find combinations for large datasets?

Tip: When working with combinations, especially with repeated elements, make sure to account for repeated sums that may result from the same elements.