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:
- (200, 314, 435, 680)
- (245, 314, 390, 680)
- (310, 314, 325, 680)
- (310, 314, 460, 545)
- (314, 360, 460, 495)
- (314, 385, 435, 495)
- (314, 385, 440, 490)
- (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:
- How can you check for unique combinations of sums?
- Can there be more than four numbers that add up to 1629?
- How do duplicate values in the list affect the total number of combinations?
- How would this problem change if some numbers were negative?
- 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