Non-standard and creative cases
A prompt that fits no familiar type, handled from first principles: clarify the objective, build a simple model, and find the levers.
Key takeaways
- Do not force a familiar framework onto an unfamiliar problem. Clarify the objective, build a simple model of the system, find the levers the model shows, and choose the cheapest one to test first.
- Any firm can use a non-standard prompt, sometimes late in a case, to see how you handle the unfamiliar.
- The strong answer builds a model from first principles and finds the real levers.
What this case type is and when it shows up
Sometimes the prompt fits no familiar type: how would you reduce waiting at a busy theme park, how should a city decide whether to allow electric scooters, how would you reduce crowding at a large religious or sports event. There is no framework to reach for, which is the point. It tests whether you can think clearly about something new.
The underlying theory, in plain language
When no type fits, go back to first principles. Clarify the objective, break the problem into your own clean parts, build a simple model of how the system works, and reason step by step.
Many of these prompts involve queues or flows, where Little's Law helps: the average wait equals the number of people in the queue divided by the rate at which people leave it (in a stable system, the arrival rate).
Stay calm and think out loud. The interviewer is watching how you handle the unknown, which matters more than any specific answer.
What the prompts sound like, from simple to hard
- Simple: how can a theme park in Abu Dhabi reduce ride queues.
- Medium: should a European city allow rented electric scooters.
- Hard: how would you reduce crowding at a large event with millions of visitors.
Finding and narrowing the real problem
Key idea
Do not force a familiar framework onto an unfamiliar problem. Clarify the objective, build a simple model of the system, find the levers the model shows, and choose the cheapest one to test first.
Frameworks for this type, each as a thinking tool with its limit
- First-principles structure: Define the goal, split the problem your own way, and reason step by step. Limit: Slower than a template, but the only honest approach when nothing fits.
- Objective and options: Name the objective, generate options, and evaluate them. Limit: Generating good options under pressure takes practice.
Methods for solving this type
- Clarify the objective
- Build a simple model of how the system works
- Use the model to find the levers
- Rank the levers by effect and cost and state your assumptions
The math patterns it relies on
- Whatever the problem needs, built from scratch
- Wait = number waiting / service rate
- Simple comparisons of options
Worked cases
Worked case
Cutting a theme-park queue
The prompt
A popular ride at a theme park in Abu Dhabi serves 1,200 people an hour, and at peak the queue holds about 2,400 people. The chart below shows the queue through the day. Roughly how long is the wait, and how would you reason about cutting it?
Interviewer-led: the interviewer shows the queue chart and asks for the peak wait, then for levers, then for which lever to test first.
Clarifying questions, with the interviewer's answers
- What is the goal: shorter waits, more riders, or happier guests?Answer: Happier guests; waits over an hour hurt the park's ratings.
- Is the ride running at full capacity?Answer: Mostly, but it stops about 10 percent of the time for safety checks.
A hypothesis to say out loud: The wait depends on how many people are ahead and how fast they are served. My hypothesis is that the fastest improvement comes from spreading peak demand, since building capacity is slow and costly.
The structure
- Wait = queue length / service rate
- Serve faster: less downtime, faster loading, more seats
- Key: Spread arrivals: timed return tickets, off-peak incentives
- Change how the wait feels: shade, entertainment, accurate signs
The exhibit
Line chart: Queue length at the ride through the day (people). Values in people in the queue. 10:00: 800; 12:00: 2,400; 14:00: 2,000; 16:00: 1,200; 18:00: 600.
Working it through
1. Estimate the wait
2,400 people in line and 1,200 served an hour.
Wait (hours):2,400 ÷ 1,200 = 22. Lever 1: remove downtime
If the ride stopped for checks outside peak hours instead, it would serve 1,200 / 0.9 people an hour at peak, and the wait would fall only a little.
Wait without downtime (hours):2,400 ÷ (1,200 ÷ 0.9) = 1.83. Lever 2: timed return tickets
If half the peak queue takes a timed return ticket instead of standing in line, 1,200 people remain, provided return slots are set in quieter hours; otherwise returners take capacity from the standby line.
Wait with timed tickets (hours):1,200 ÷ 1,200 = 14. Where the quiet hours are
Read the chart: at 18:00 only 600 people are queuing, a wait of about 30 minutes, so return slots belong in the late afternoon and evening.
Wait at 18:00 (minutes):600 ÷ 1,200 × 60 = 30
What the exhibit shows
The queue is four times longer at midday than in the early evening, so there is quiet capacity later in the day to move guests into.
The recommendation
Pilot timed return tickets first, and move safety checks out of peak hours in parallel. First, the wait is about two hours, and removing downtime alone cuts it only to about 1.8 hours. Second, timed tickets for half the peak queue cut the physical wait to about one hour at low cost, provided return slots are set in quieter hours; otherwise returners take capacity from the standby line. Third, the chart shows those quieter hours exist: by 18:00 the queue is only 600 people, a wait of about 30 minutes. Beyond these two structural levers, a third changes how the wait feels: shade, entertainment, and accurate wait-time signs.
Risks: Guests may dislike booking return times; Timed tickets can move the crowd to other rides.
Next steps: Pilot timed tickets on this ride for two weekends; Measure guest ratings before and after.
A strong candidate
Built a simple model from scratch, used it to find and size the levers, and picked a cheap pilot first.
A weak candidate
Listed random ideas (music, an app, more staff) with no model and no sense of which would help most.
Worked case
Crowding on a Tokyo rail platform
The prompt
A Tokyo rail operator has dangerous crowding on one station platform during the morning peak. How would you think about fixing it?
Candidate-led: there is no framework for this. You build your own flow model and ask for the numbers; the interviewer answers and challenges.
Clarifying questions, with the interviewer's answers
- What exactly is the problem: safety, delays, or passenger comfort?Answer: Safety first. When the platform is too full, staff must close the ticket gates, which causes delays across the line.
- How many people can the platform hold safely?Answer: About 1,500.
- Is this every weekday, and for how long?Answer: Every weekday, for about one hour of the morning peak.
A hypothesis to say out loud: A platform fills up when people arrive faster than trains take them away. My hypothesis is that trains cannot carry the peak flow, so people build up on the platform, and that moving some trips out of the peak is cheaper than adding train capacity.
The structure
- People on the platform = arrivals minus people the trains take away
- Arrivals per hour at the peak
- Key: Train capacity: trains per hour x free space per train
- Levers: more trains, longer trains, or fewer peak arrivals
- Cost and speed of each lever
Working it through
1. Train capacity
Candidate: "How often do trains come, and how many people can each take from this station?" Interviewer: "One every 3 minutes, with room for about 800 more passengers each."
Passengers the trains can take (per hour):60 ÷ 3 × 800 = 16,0002. The gap
Interviewer: "About 18,000 people arrive in the peak hour." Candidate: "Then about 2,000 more people arrive each hour than the trains can take."
Excess arrivals (per hour):18,000 - 60 ÷ 3 × 800 = 2,0003. People on the platform
Between trains, about 900 people arrive; over the hour, the extra 2,000 build up on top. That is almost twice the safe limit of 1,500.
People waiting at the end of the peak:18,000 ÷ 20 + (18,000 - 60 ÷ 3 × 800) = 2,9004. How many trips must move
Candidate: "To stay within train capacity, this share of peak trips would have to move outside the peak."
Share of peak trips to move (%):(18,000 - 16,000) ÷ 18,000 × 100 = 11.115. Cost of an off-peak discount
Candidate: "What if people who enter this station before 7:30 get JPY 40 off that morning trip?" Interviewer: "About 5,000 people already travel then and would get it too, and we run about 245 working days a year."
Yearly cost of the discount (JPY):(2,000 + 5,000) × 40 × 245 = 68,600,0006. Compare with more trains
Interviewer: "A new signaling system would allow a train every 2.5 minutes, for about JPY 3 billion." Candidate: "That is the cost of more than 40 years of the discount."
Years of discount equal to the signaling cost:3,000,000,000 ÷ ((2,000 + 5,000) × 40 × 245) = 43.73
The recommendation
I recommend an off-peak fare incentive and better crowd control now, with the signaling upgrade kept in the long-term plan. First, trains can take about 16,000 people an hour but 18,000 arrive, so about 2,900 are waiting by the end of the peak. Second, moving about 11 percent of peak trips closes the gap, and a JPY 40 early-travel discount costs about JPY 69 million a year. Third, the upgrade costs as much as more than 40 years of the discount, so it makes sense only if demand keeps growing. Test the discount for three months.
Risks: Fewer people may change their travel time than needed, because work start times are fixed; Crowding may move to the next station on the line; Peak demand may keep growing, bringing the upgrade forward.
Next steps: Ask the three largest employers near the station about flexible start times; Run the discount trial and track arrivals every five minutes; Include the signaling upgrade in the five-year investment plan.
A strong candidate
Built a flow model with no framework, found the exact gap, turned it into the number of trips to move, and compared a cheap lever with an expensive one on cost.
A weak candidate
Suggested more staff to push passengers onto trains and nicer signs, with no model of why the platform fills up.
Prompt: "How would you reduce this queue?"
Weaker answer
Offers ten ideas (more staff, an app, signs, music) with no model of what drives the wait.
Stronger answer
Estimates the wait from queue length and service rate, uses the model to size three kinds of lever, and picks timed tickets as the cheap first pilot.
Why the stronger answer wins: The strong answer builds a model from first principles and finds the real levers. The weak one brainstorms without understanding the system.
Common mistakes, traps, and curveballs
- Forcing a familiar framework onto a new problem
- Freezing because no template fits
- Over-engineering a simple question
- Refusing to commit to an answer
- Treating the first two levers found as the only ones
Any firm can use a non-standard prompt, sometimes late in a case, to see how you handle the unfamiliar. Calm, first-principles reasoning is what is being tested. Formats differ by office and change over time, so check the current process for your target office.
Practice
A bank branch in Singapore serves 40 customers an hour and has 20 people waiting. About how long is the wait, in minutes?
A stadium in the Gulf holds 60,000 fans. It has 20 exit gates, and each gate lets out about 1,500 people an hour. How many hours does it take to empty?
A food truck in Sydney serves one customer every 90 seconds, and 12 people are in line. About how long does the last person wait, in minutes?
An interviewer asks where a growing city should put its next fire station, a question that fits no case type. What is the best first step?
You built a model and the interviewer says one of your inputs is wrong. What is the strongest response?
Asked how many ambulances a city needs, what is the best first step?
When nothing fits, clarify the objective, build a simple model of the system, and let the model show you the levers.
Sources for this lesson (1)
- Recognized public explanations of case-interview concepts and frameworks
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