Calculator
Example Data Table
| Permutation value | r | Found n | Check |
|---|---|---|---|
| 20 | 2 | 5 | 5P2 = 5 × 4 = 20 |
| 120 | 3 | 6 | 6P3 = 6 × 5 × 4 = 120 |
| 840 | 4 | 7 | 7P4 = 7 × 6 × 5 × 4 = 840 |
About This Calculator
This calculator helps you find the unknown value of n when a permutation value and r are already known. In many combinatorics questions, you are given nPr and asked to recover the original set size. That step can be slow when you test values by hand. This page automates the search and shows each candidate clearly.
The tool works with positive whole-number permutation values. It searches integer values of n from your chosen starting point and checks the permutation product exactly. Because the comparison uses exact whole-number multiplication, the answer is not estimated from decimals. That makes it useful for algebra work, exam practice, and verification tasks.
Formula Used
The standard permutation formula is nPr = n! / (n - r)!. For fixed r, this simplifies to a descending product of r terms. For example, nP3 becomes n × (n - 1) × (n - 2). To find n, the calculator tests valid integers and compares each computed product with the target permutation value.
This method is reliable because nPr increases as n increases, provided r stays fixed and n is at least r. Once a tested value becomes larger than the target, later values will also be larger. That allows the search to stop early and keeps the result efficient.
How to Use This Calculator
Enter the known permutation value in the first box. Enter r in the second box. Then choose a starting value for n and a maximum value to test. The graph span controls how many nearby n values appear on the plot. After submission, the result appears above the form, followed by a working table and graph.
Use the CSV button when you want a compact result sheet. Use the PDF button when you need a printable copy. The example table below the calculator gives quick reference cases, and the graph helps you see how fast permutation values rise around the answer.
FAQs
1. What does this calculator solve?
It finds an integer n when the permutation value nPr and r are known. The tool checks candidates in order and returns the exact n that satisfies the permutation equation.
2. What if no answer appears?
If no exact match exists, the target value does not equal nPr for any tested integer in your selected range. Increase the maximum n or recheck your inputs.
3. Can r be larger than n?
No. A permutation requires selecting r items from n items, so n must be at least r. The calculator automatically starts from r if you enter a smaller starting value.
4. Why are only integer answers returned?
Permutation counts describe arrangements of whole items. Because of that, n is normally treated as a whole number in combinatorics problems, so the calculator searches only integer candidates.
5. What does the graph show?
The chart plots nearby n values against log10(nPr). A logarithmic scale keeps the visual readable, especially when permutation values grow very quickly around the solution.
6. Can I export my result?
Yes. The CSV export gives a quick data file, and the PDF export creates a clean report with the summary and working table from your current calculation.
7. Is the computation exact or rounded?
The search uses exact whole-number multiplication for the permutation values it tests. That avoids decimal rounding during the core comparison stage of the calculation.
8. When is this calculator useful?
It is useful in algebra, counting principles, competitive exams, discrete mathematics, and homework checks whenever a problem gives nPr and r but leaves n unknown.