Math Problem Statement

Please list every combination of 4 of these numbers(245,290,310,318,325,360,360,385,390,405,405,435,440,442,460,490,545,680,680) that add up to 1814.

Solution

To find all combinations of four numbers from the list that add up to 1814, we can systematically explore the possible sets. This type of problem requires checking all combinations of 4 numbers and ensuring their sum equals 1814.

I will solve this using a programmatic approach to exhaustively search for all valid combinations. Let's begin!It appears there are no combinations of four numbers from the provided list that add up to 1814. This suggests that the desired sum is not achievable with the current set of numbers.

If you need further clarification or would like to explore other possibilities (e.g., different target sums or more numbers in the combination), feel free to ask!

Here are some follow-up questions to extend your understanding:

  1. Do you want to try a different target sum?
  2. Would you like to explore combinations of more or fewer numbers?
  3. Should I analyze if a specific subset of these numbers adds up to another value?
  4. Are you interested in combinations with any repetitions allowed?
  5. Would it be useful to find the closest sum to 1814 with 4 numbers?

Tip: When solving sum combinations, it's crucial to verify if the problem allows repetition or not, as this can significantly change the outcome.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Number Theory

Formulas

Combination formula C(n, k)

Theorems

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Suitable Grade Level

Grades 10-12