Calculator
This tool builds balanced groups and counts how many distinct presentation plans exist, using partitions, permutations, and timing arithmetic.
Example data table
A sample input set and its computed schedule fields. Change values above to match your setting.
| Participants | Target size | Topics | Minutes/group | Transition | Session | Groups (k) | Total minutes |
|---|---|---|---|---|---|---|---|
| 24 | 4 | 10 | 7 | 2 | 60 | 6 | 52 |
| 18 | 3 | 6 | 6 | 1 | 45 | 6 | 41 |
| 30 | 5 | 12 | 8 | 2 | 90 | 6 | 58 |
Formula used
- Balanced group sizes: choose k groups so sizes differ by at most 1.
- Unlabeled balanced groupings count:
N! / ( (b!)^{n_b} · (s!)^{n_s} · n_b! · n_s! )Here, b is the bigger size, s is the smaller size, and n_b + n_s = k.
- Topic assignments:
Without repetition: P(T,k) = T! / (T − k)!With repetition: T^k
- Presentation sequences: k! if order matters, otherwise 1.
- Total distinct plans: groupings × topic assignments × sequences.
- Total time: k·p + (k−1)·t where p is minutes/group and t is transition minutes.
- Sessions needed: ceil(total_time / session_minutes) when session minutes > 0.
How to use this calculator
- Enter the number of participants and choose a planning method.
- Set topic rules, then decide whether order matters.
- Enter minutes per group, transition time, and session length.
- Enable the example plan and choose a seed for repeatability.
- Click Calculate to view results above the form.
- Use Download buttons to export CSV or PDF summaries.
Balanced grouping design
Planning balanced group sizes starts with N participants and a target size or group count. The calculator builds k groups so sizes differ by at most one, keeping discussion time and workload equitable. When N is not divisible by k, it creates n_b groups of size b and n_s groups of size s, where b=s+1 and n_b+n_s=k. This structure is the baseline for estimating time, topics, and overall plan variety. It also flags infeasible inputs early.
Counting distinct grouping outcomes
To quantify how many different ways you can split people, the tool uses a combinatorial count for unlabeled balanced groupings: N! divided by repeated factorial terms for equal-size groups and for the number of groups with the same size. This prevents double‑counting when groups are interchangeable. Even modest classes can produce astronomically large counts, so results are reported with exact integers when small and scientific notation with digit estimates when large. This keeps reporting stable.
Topic assignment scenarios
Topic planning adds another layer. If topics must be unique, assignments follow permutations P(T,k)=T!/(T−k)!, which requires T≥k. If repetition is allowed, assignments become T^k, enabling reuse of high‑value themes across groups. Combine topic assignments with grouping counts to see whether variety is driven more by rearranging people or by rotating topics. This helps instructors decide if adding topics meaningfully increases diversity of presentations. It supports quick what‑ifs.
Scheduling and session budgeting
Time estimates follow a simple but practical model: total minutes = k·p + (k−1)·t, where p is minutes per group and t is transition time and breaks. If a session limit is provided, the calculator reports sessions as ceil(total/session). With an optional start time, it produces a timetable so facilitators can announce exact start and end slots. This is useful when you need to fit presentations into a single class period or multiple lab sections.
Fairness checks and repeatable plans
Beyond counts, the calculator reports fairness indicators such as the group-size range and the standard deviation of sizes. A near‑zero deviation signals that no team is disproportionately large. For reproducible planning, the example plan generator accepts a seed, producing the same grouping and order on reruns—handy for audits or reprinting schedules. Use these outputs to justify decisions, communicate expectations, and reduce disputes about perceived bias over time.
FAQs
1) How are groups balanced when N does not divide evenly?
Groups are split so sizes differ by at most one. The tool creates some groups with size s and the remaining with size b=s+1, keeping workloads and speaking time as even as possible.
2) What does “unlabeled groupings” mean here?
It counts partitions where swapping whole groups does not create a new outcome. This avoids double-counting identical group sets that only differ by group names or table positions.
3) When should I allow topic repetition?
Allow repetition when you have fewer topics than groups or when you want multiple teams on the same theme for comparison. Choose unique topics when you need maximum coverage and T is at least k.
4) Why are some results shown in scientific notation?
Combinatorial counts grow factorially, so the exact integer can exceed practical display length. The calculator shows digits and a mantissa for large values, and switches to exact integers when the count is small enough.
5) How is the schedule time calculated?
Total time equals k·minutes_per_group plus (k−1)·transition_minutes. If you enter a session limit, the tool reports the number of sessions using a ceiling division and can generate time slots from an optional start time.
6) Can I reproduce the same example plan later?
Yes. Enter the same random seed and inputs to regenerate the identical grouping, order, and timetable. Use the download buttons to export a CSV summary or a printable PDF for sharing.