← Research lab92 · Analytical complexity benchmark

Group bada ho, toh hisaab kitni fast complex hota hai?

Adding one person does more than add one balance. That person can interact financially with every existing member, so the number of possible pair relationships follows n × (n − 1) ÷ 2.

Analytical benchmarkReviewed 16 October 2026
66

possible pairs at 12 people

Every unique person-to-person relationship.

11×

growth from 4 to 12

Six possible pairs become sixty-six.

12

members supported per group

Current Karja group limit across plans.

Results

Model ka output.

Group sizePossible pairsPairs per personvs 4-person group
4 people

6

3

1.0×

6 people

15

5

2.5×

8 people

28

7

4.7×

12 people

66

11

11.0×

Sample

Exactly kya analyse hua?

Group sizes from 2 through 12 people; the displayed checkpoints are 4, 6, 8 and 12.

Method
  1. 01

    Treat each unique pair of members as one possible balance relationship.

  2. 02

    Calculate combinations using n × (n − 1) ÷ 2.

  3. 03

    Compare each result with the 4-person baseline.

  4. 04

    Do not assume every possible pair becomes active.

What we learned

Findings ko context mein padho.

  • Relationship count grows faster than headcount.
  • A structured ledger becomes more valuable as different people alternate as payer.
  • Net balances prevent the interface from exposing every possible pair as a separate manual calculation.
Quick answers

Study FAQs.

Why are there 66 possible pairs in a 12-person group?

Each member can pair with eleven others, but every pair would otherwise be counted twice. The calculation is 12 × 11 ÷ 2 = 66.

Does a larger group always need more transfers?

Not necessarily. Net settlement can keep the final transfer list much shorter than the number of possible relationships.