cs-133 — The Late Bus Ledger

Problem

The university shuttle poster says: "a bus every ten minutes." The operational facts:

• Departures from the depot are scheduled at :00, :10, :20, :30, :40, :50.
• One loop — depot → stop A → stop B → stop C → depot — takes exactly 25 minutes (legs: 4, 6, 7, 8).
• The fleet is two buses. A bus departs only when it is back at the depot; a bus that returns late departs late.

Your deliverables:

1. The actual depot departure times for the first six scheduled slots.
2. The gap between consecutive departures for those slots.
3. The verdict: does "a bus every ten minutes" hold, and if not, exactly which gaps break it?
4. The two-sentence notice to students that is honest — no cheerleading, no excuses.

If the problem is ambiguous anywhere, state the assumption you are making and carry on — a stated assumption is part of a good answer.

Examples

• Input: the schedule, loop legs, fleet size
• Output: departures 0, 10, 25, 35, 50, 60 — gaps 10, 15, 10, 15, 10 — verdict + notice

Solve for the worked instance first. Then ask what would change if one number, name, or condition were replaced by something stranger.

What to notice

• Departure slots are a wish; the fleet is the constraint. The actual departure is max(scheduled, back-at-depot time).
• Once one departure slips, every later gap inherits the slip — lateness propagates through the schedule like a carried error.
• The fix is arithmetic, not driving faster: a loop of 25 minutes with headway 10 needs a fleet of at least ⌈25/10⌉ = 3.

Discussion starter

After the solution is revealed, the class spends five minutes on this prompt: "Operations proposes shortening the loop by three minutes instead of buying a third bus. Does the poster claim become true? Show the departure ledger that decides it."

Constraints and assumptions

• Difficulty: Foundational (multi-step schedule reasoning).
• Topics: scheduling, communication, assumptions.
• Legs are exact (no traffic variance) — this is a timetable claim, checked arithmetically.
• Classroom-scale inputs unless the problem says otherwise.
• Time-box: about five minutes for a first attempt; partial answers with clear reasoning are worth more than silent struggling.
• Optional stretch (not required): describe an alternative approach and say when it beats the obvious one.

Hints and extension

• First nudge: write the return time of the bus that left at :00 before worrying about any other slot.
• If stuck after three minutes, write the input/output line you expect and trace the smallest example by hand.
• After the reveal, attempt the extension below before the next lecture.
• Extension challenge: with a three-bus fleet, find the loop length at which the ten-minute promise breaks even at the depot.