Math Problem Statement

Please list every combination of 4 of these numbers(200,245,290,300,310,318,325,360,385,390,435,440,442,460,490,545,670,680,680) that add up to 1814.

Solution

To find all combinations of 4 numbers from the list that add up to 1814, I will compute this through a methodical search. I'll generate the combinations and identify those that satisfy the condition where their sum equals 1814.

Let me compute this for you.There are no combinations of 4 numbers from the provided list that add up to 1814. It seems that no subset of four numbers satisfies the sum condition.

Would you like to modify the list of numbers or the target sum to explore other possibilities? Here are five related questions that could expand the topic:

  1. Would you like to explore combinations of 5 numbers that sum up to a specific target?
  2. Can I help you explore other methods for solving combinatorial problems?
  3. Would you like to understand the concept of combinations more deeply?
  4. Should I find subsets of the list that approximate 1814 as closely as possible?
  5. Would you prefer to explore combinations with different constraints, like using fewer numbers?

Tip: When dealing with combinatorial problems, the number of elements and the constraints (like a target sum) significantly affect the number of possible combinations.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Sum of Subsets

Formulas

Combination Formula: nCr = n! / [r!(n-r)!]

Theorems

No specific theorems, but general principles of combinatorics and subset sums

Suitable Grade Level

Grades 10-12