Please list every combination of 4 of these numbers(200,245,290,300,310,314,318,325,360,360,385,390,405,405,435,440,442,460,490,495,545,670,680,680) that add up to 1629.

Let's approach this problem methodically.

We need to find **all combinations** of four numbers from the given list that add up to **1629**. The numbers you provided are:

\[ \{200, 245, 290, 300, 310, 314, 318, 325, 360, 360, 385, 390, 405, 405, 435, 440, 442, 460, 490, 495, 545, 670, 680, 680\} \]

Since this problem involves finding sums of multiple combinations, I will calculate it programmatically to ensure accuracy and avoid missing any possible combinations.

Let me compute this for you.Here are the combinations of four numbers that add 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 repeated numbers in the original list.

Would you like further details or explanations on how the combinations were found?

Here are five relative questions to expand on this topic:
1. How do combinations differ from permutations in mathematics?
2. Can you explain the difference between combinations with and without replacement?
3. What are some practical applications of combination sums in real life?
4. How does dynamic programming help in solving complex combination sum problems?
5. What is the complexity of finding combinations that satisfy a given condition?

**Tip:** When solving combination problems, reducing the set of possible candidates early on (by removing numbers that can't participate in the sum) can save time!

Please list every combination of 4 of these numbers (200, 245, 290, 300, 310, 314, 318, 325, 360, 360, 385, 390, 405, 405, 435, 440, 442, 460, 490, 495, 545, 670, 680, 680) that add up to 1629.

Explore how to find all combinations of four numbers from a given list that add up to 1629. This detailed solution involves combinatorics and subset selection, suitable for high school students learning algorithmic problem solving.

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