Please find every combination of 4 of these numbers(245,290,300,309,310,318,325,350,360,360,385,390,405,405,435,440,442,460,490,495,525,545,680,680) that add up to 1629.

To find every combination of four numbers from the given set that add up to 1629, I will systematically check the sums of all unique combinations of four numbers. The provided set of numbers includes some duplicates, which I will account for in the combination process.

Let me calculate this and find the correct combinations.

I'll be back shortly with the result.The combinations of four numbers from the given set that add up to 1629 are as follows:

1. (290, 309, 350, 680)
2. (300, 309, 495, 525)
3. (309, 360, 435, 525)
4. (309, 385, 390, 545)
5. (309, 385, 440, 495)
6. (309, 390, 405, 525)
7. (309, 390, 435, 495)
8. (309, 390, 440, 490)

Some combinations appear more than once due to duplicate numbers in the original set.

Would you like further details or have any questions? Here are five related questions for expanding your understanding:

1. How many unique combinations can you form from the set of numbers?
2. What is the impact of duplicates in such combination problems?
3. How can you generalize this method for different target sums?
4. Can you form a formula to calculate how many combinations add up to a specific number?
5. How would this approach change for larger or smaller sets?

**Tip**: Using efficient algorithms such as dynamic programming can speed up finding combinations in larger datasets.

Discover all possible combinations of four numbers from the set (245, 290, 300, 309, 310, 318, 325, 350, 360, 360, 385, 390, 405, 405, 435, 440, 442, 460, 490, 495, 525, 545, 680, 680) that sum to 1629. This problem involves combinatorics and number theory, offering insight into mathematical addition and efficient solution methods. Suitable for students in Grades 10-12.

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