Math Problem Statement

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.

Solution

To find every combination of four numbers from the list that adds up to 1629, I will check the various subsets of four numbers and calculate their sum to see which ones satisfy the condition.

Here is the complete list of numbers provided: 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 will now work on computing the combinations. Please hold on.Here are the combinations of four numbers from your list that sum 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)

These combinations appear multiple times due to duplicate values in the list.

Would you like more details or have any questions?

Here are some related questions:

  1. How can you check for unique combinations of sums?
  2. Can there be more than four numbers that add up to 1629?
  3. How do duplicate values in the list affect the total number of combinations?
  4. How would this problem change if some numbers were negative?
  5. How does this method scale for larger lists or higher target sums?

Tip: When working with combinations, remember that repeated numbers can lead to the same result multiple times.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Addition
Subset Sums

Formulas

Sum of subsets formula (n choose k) for combinations
Basic addition

Theorems

Combination formula: C(n, k) = n! / (k!(n - k)!)

Suitable Grade Level

Grades 10-12