Step 1: Target the goal of prophylaxis. After a meningococcal case, close contacts must be cleared of nasopharyngeal carriage. The agent that does this and is the classic answer is rifampicin.
Step 2: Remember the schedule. Rifampicin is dosed by weight - 5 mg/kg for infants below 1 month, 10 mg/kg above - taken orally twice daily for 2 days, and avoided in pregnancy.
Step 3: List backups for special groups. When rifampicin is unsuitable, ceftriaxone given intramuscularly as a single dose (125 mg if under 15, 250 mg if over 15) or a single 500 mg oral dose of ciprofloxacin (adults over 18) can be used.
Step 4: Exclude the wrong drugs. Penicillin treats invasive disease but does not reliably eradicate carriage; chloramphenicol and tetracycline are not first-line prophylaxis here. Hence rifampicin stands.
\[\boxed{\text{Rifampicin}}\]