Math Problem Statement

Find all combinations of 2 of these numbers(1,2, 2, 3) that add up to 4

Solution

We are tasked with finding all unique combinations of two numbers from the set {1,2,2,3}\{1, 2, 2, 3\} that add up to 4.

Step-by-step approach:

  • First, list all possible pairs of two numbers: (1,2),(1,2),(1,3),(2,2),(2,3),(2,3)(1, 2), (1, 2), (1, 3), (2, 2), (2, 3), (2, 3)
  • Now, check which pairs sum to 4:
    1. 1+2=31 + 2 = 3 (does not work)
    2. 1+2=31 + 2 = 3 (does not work)
    3. 1+3=41 + 3 = 4 (works)
    4. 2+2=42 + 2 = 4 (works)
    5. 2+3=52 + 3 = 5 (does not work)
    6. 2+3=52 + 3 = 5 (does not work)

Conclusion:

The pairs that sum to 4 are:

  • (1,3)(1, 3)
  • (2,2)(2, 2)

These are the two unique combinations.

Would you like more details or have any other questions?


Here are 5 related questions:

  1. How would the process change if the set had more numbers?
  2. What if you needed to find combinations that sum to a different value, like 5?
  3. How would the solution change if the numbers had to be distinct?
  4. Can you generalize this approach for larger sets of numbers?
  5. What happens if you need to find combinations of 3 numbers?

Tip: When solving problems with combinations, make sure to avoid counting the same pair more than once if order does not matter.

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Math Problem Analysis

Mathematical Concepts

Combinatorics
Addition
Set Theory

Formulas

Sum of two numbers a + b = 4

Theorems

Combination without repetition

Suitable Grade Level

Grades 5-7