NUMBER LAB · EXPLORE WITH CONFIDENCE

Integer Partition Explorer

Count unordered ways to write an integer as a sum, restrict the largest part or require distinct parts, and export bounded examples.

Worked examplesBrowser processingTXT · CSV · JSON

Explore the example, or adjust the inputs. Save a project to keep your settings.

A useful starting point

5 has 7 unordered partitions. With distinct parts only, the partitions are 5, 4 + 1 and 3 + 2.

Scope and limits

Totals and largest parts 1–150. Exact full count; listing and downloads contain at most 1,000 examples, not every partition for large totals.

Calculations run in your browser. Projects are saved only when you download them. Website advertising and analytics follow the privacy and consent settings. Import large integer CSV columns as text in spreadsheets to preserve their digits.

Using Integer Partition Explorer

Count unordered ways to write an integer as a sum, restrict the largest part or require distinct parts, and export bounded examples.

Choose a worked example or enter your own values in the labeled controls.
Adjust the available options. Results refresh when you leave a field or choose an option.
Review the result summary, interpretation and calculation table. Check any explicit limits or assumptions.
Copy the text or download TXT, CSV or JSON. Save a project to reopen the same inputs later.

Example

5 has 7 unordered partitions. With distinct parts only, the partitions are 5, 4 + 1 and 3 + 2.

Questions & answers

Are 2 + 3 and 3 + 2 different?

No. Partitions ignore order. This tool does not enumerate ordered compositions.

Why are fewer examples listed than the count?

The exact count is calculated separately. Listing and export use your selected cap of up to 1,000 examples so large counts do not freeze the page.

Can I save and reopen my settings?

Yes. Save project downloads a JSON file for this tool. Open project restores it; undo and redo work during the current session.

Does the table contain every result?

The table is paginated in groups of 50. Downloads contain all listed rows. The partition tool intentionally caps its example listing while reporting the full exact count.