From the mathematics of combinatorics, running from Blaise Pascal (Traité du triangle arithmétique, 1665) through Jacob Bernoulli (Ars Conjectandi, 1713) and Leonhard Euler (Introductio in analysin infinitorum, 1748).
Counts and lists every combination in a decision or test space, using multiplication, permutations, and combinations, so no case is missed and the size of the space is known.
When to reach for it
When a decision turns on covering all the cases, as in test plans, eligibility rules, or audits, or when a search may be too large to finish.
How it runs
- List the dimensions that vary independently.
- Count the possible values on each dimension.
- Decide whether order matters, then multiply, permute, or combine.
- Compute the total and judge whether full coverage is feasible.
- If it is not, sample or prune the space on purpose.
Where it sits in SOLVE eX
Go to the source
- Traité du triangle arithmétique, written 1654, 1665
- Ars Conjectandi, 1713
- Introductio in analysin infinitorum, 1748