Definition
Systematic search
A systematic search checks possible cases in an organised way so none are missed or repeated.
What it means
Choose an order and keep a record. Check each possibility once, cross out branches that cannot work, and know why the list is complete. Random trying may find an answer; a systematic search can show that you found all answers or that none exist.
Remember it
Order, record, rule out, complete.
Example
To find every factor pair of 36, test first factors in order: 1, 2, 3, 4, 5, 6. Record 1 × 36, 2 × 18, 3 × 12, 4 × 9, skip 5, and stop at 6 × 6 because later pairs would repeat earlier ones.
Watch for
The search space must be defined; checking many cases is not enough unless the method shows that none were skipped.
Common mix-up
Systematic does not mean slow—it means the order and stopping rule are justified.
Exact meaning
A systematic search is an ordered method for examining a defined set of possibilities, recording progress and using constraints to avoid omissions, duplicates, and impossible cases.