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Combination Sum Calculator

Find all possible number combinations that add up to a specific target value. Useful for math learning, programming practice, budgeting, and puzzle solving.

All Combinations
Find every valid combination
Flexible Options
Allow reuse or use once
Quick & Accurate
Instant results with precise calculations
🔢 Find all number combinations that sum to your target value

Combination Sum Calculator

Enter a list of numbers and a target sum. The calculator will find all possible combinations that add up to the target.

Enter numbers separated by commas

ON

When ON, numbers can be used multiple times. When OFF, each number can only be used once.

Check this to allow numbers to be repeated in combinations. This is synchronized with the toggle above.

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How to Use Combination Sum Calculator

Step-by-Step Instructions

The Combination Sum Calculator helps you find all possible number combinations that add up to a specific target value. This tool is useful for math learning, programming practice, budgeting, and puzzle solving.

Step 1: Enter Numbers

In the Numbers field, enter the numbers you want to use, separated by commas. For example:

  • 2, 3, 6, 7 - Enter numbers with commas between them
  • You can enter any positive numbers
  • Spaces around commas are optional (2,3,6,7 or 2, 3, 6, 7 both work)

Step 2: Enter Target Sum

In the Target Sum field, enter the value you want the combinations to add up to. This is the target total you're looking for.

Step 3: Choose Number Reuse Option

Toggle the Allow Number Reuse option:

  • ON (Checked): Numbers can be used multiple times in a combination. For example, if you have [2, 3] and target is 6, you can use 2+2+2=6 or 3+3=6.
  • OFF (Unchecked): Each number can only be used once per combination. For example, if you have [2, 3, 6, 7] and target is 7, valid combinations are [7] or [2, 2, 3] (if reuse is ON), but not [2, 5] (5 doesn't exist).

Step 4: Calculate

Click the Calculate button to find all combinations. The calculator will:

  • Display the total number of valid combinations found
  • Show each combination that sums to the target
  • List all combinations in an easy-to-read format

Understanding the Results

The results show:

  • Total Combinations Found: The number of unique combinations that sum to the target
  • Combination List: Each valid combination displayed with the numbers that add up to the target

Combinations are displayed in a format like: [2, 2, 3] which means 2 + 2 + 3 = 7

Example Calculation

If you enter:

  • Numbers: 2, 3, 6, 7
  • Target Sum: 7
  • Allow Reuse: ON

The calculator will find combinations like:

  • [7] - Single number equals target
  • [2, 2, 3] - 2 + 2 + 3 = 7
  • [2, 5] - Not valid (5 is not in the list)

If Allow Reuse is OFF, only combinations using each number at most once are shown.

Using the Fill Example Button

Click the Fill Example button to see a sample calculation with pre-filled data (Numbers: 2, 3, 6, 7, Target: 7). This helps you understand how the calculator works.

Tips for Best Results

  • Use Positive Numbers: The calculator works best with positive integers or decimals
  • Reasonable Target: Very large targets with many numbers may take longer to calculate
  • Clear Input: Make sure numbers are properly separated by commas
  • Reuse Option: Enable reuse for more combinations, disable for unique combinations only
  • No Duplicates: The calculator automatically handles duplicate numbers in your input

Common Use Cases

  • Math Learning: Practice finding number combinations that sum to a target
  • Programming Practice: Understand combination sum algorithms
  • Budgeting: Find combinations of expenses that total a specific amount
  • Puzzle Solving: Solve number puzzles and brain teasers
  • Problem Solving: Explore different ways to reach a target value

How the Algorithm Works

The calculator uses a backtracking algorithm to find all valid combinations:

  • It tries each number in the list
  • If the number can be added without exceeding the target, it's included
  • The process continues recursively until the target is reached or exceeded
  • All valid paths that sum to exactly the target are collected
  • Duplicate combinations are automatically removed