Brainteaser: Birds on train

Hey,

I am new to this too, but I think I have some ideas for your problem.

Your approach looks good, but I think you have a mistake in how you time the trains. You say that there is one train every three stations and that it takes 1m30s to travel the distance from one station to the next. But how long does the train spend at each station?

My approach would be to represent each line as a timeline (the time it would take one train to go from one side to the other). All the trains on the line in a given direction should then be distributed evenly along this timeline in increments of the "average time between trains" + "waiting time at the station" as you already did.

Assumptions:

• 1m 30s travel time between stations
• 1m 00s waiting time per station
• 3m 00s between trains
• 21 Stops per line
• 14 lines

Based on these assumptions we take a total of 2m30s per stop. Now I would also assume that the trains changing direction at the end of the line take the equivalent of one stop to do so, so let's change the average amount of stops per line to 22.

Now the length of our timeline can be calculated as 22stops * 2m30s = 55min.

If there is a train every 3 min we can round the number of trains per leg to 14 (55min/(3min+1min)).

So the total number of trains would now be 14 trains per leg * 2 legs * 14 lines = 392 trains.

Obviously, the assumptions make a major difference, so changing the time between trains to 2min will lead to 504 trains at peak time.

Hope that helps!

Hi Anonymous,

there may be several reasons for that; some of them, in order of frequency, are:

1. Your structure is not complete enough – you are just using not MECE/ not complete structure
   • Solution: Victor Cheng Look Over My Shoulder, MBA Handbooks, PrepLounge Resources section, Expert sessions
2. You have to develop more business acumen – your structure is fine, however you are unable to brainstorm based on the structure:
   • Solution: case reading, eg from MBA Handbooks, ideally focused on the topic you have to improve
3. You are unable to prioritize key points in your structure and try to cover all the details eg presenting up to the forth layer in your initial structure
   • Solution: Time yourself when presenting a structure (eg initial one should take max 1.5-2mins) to learn to focus on the essential points only
4. You are not listening to the hints of the interviewer
   • Solution: Commit to always repeat the question the interviewer is asking
5. You don’t know how to approach correctly math questions
   • Solution: (i) define the formula you want to use upfront; (ii) verify the formula with the interviewer; (iii) add the numbers just once the forumla has been verified. If you are slow on the math part, train on percentages/divisions in particular
6. Your framework is MECE but you are unable to eliminate useless branches of the framework
   • Solution: learn how to draw a more clear issue tree, commit to an area and graphically eliminate it each time you find it is a dead end
7. You lack live case interview experience. All the previous points are fine, but you just spend a lot of time in writing down your approach, considering the best option, eliminate areas, etc due to lack of live experience and/or pressure.
   • Solution: P2P interviews on PrepLounge

Best,

Francesco

Hi Anonymous,

first of all - this is not a brain teaaser, but an ordinary estimation question! Here is a high-level approach:

I would start with the second question, because it is most straight forward:

1. Clarify the required generation capacity in France (a Gigawatt figure)

2. Clarify the generation capacity per square meter of solar panel

3. Divide 1 by 2

Regarding the first question:

1. Brainstorm a list of facilities where solar panels can be installed (of course roofs, but there might be additional areas)

2. Estimate a maximum percentage for each kind of installation facility that can be used for solar panel installations

3. Estimate the average installation area (in sqm) available for each facility type

4. Estimate the number for each facility type (e.g. number of roofs in France)

5. Multiply 4 with 3 and with 2 for each facility type and add up the results. This is the overall (potential) installation area of solar panels in France (in sqm). Since a panel has 1 sqm size, this is also the number of panels.

Cheers, Sidi

Hey there

Here is one approach:

# Hair Salons = (# hours required for men's haircuts per year + # hours required for women's haircuts per year) / average service capacity of 1 hair salon (which would be: opening hours x average # hair dressers x utilization rate).

Reasoning

I usually like to estimate these from the demand side - the logic being that a sizing of demand is actually an estimate of the maximum efficient supply of hair salons that can be supported in the market. Estimating it from the supply side is also a great approach, but you leave yourself open to the risk that there is undersupply in the market.

High level illustration (you can add more segments to this)

Total service hours required for haircuts p.a.:

• Assume 8m people in NY; 4m men and 4m women
• Service hours for men:
  • Assume men go to hair salon average once every month, 30min each time
  • Service hours p.a. = 4m x 12 x 0.5 = 24m hours
• Service hours for women:
  • Assume women go to hair salon average once every 3 months, 1 hours each time
  • Service hours p.a. = 4m x 4 x 1 = 16m hours
• Total time spent in hair salons is 40m hours p.a. in NY

Total service capacity per hair salon

• Assume 8 hours operating time, average 3 hair dressers, 50% utilization rate, open 6 days per week for 50 weeks.
• Note: the key assumption here is that a hair dresser cannot work
• Hence service hours per hair salon p.a. = 8 x 3 x 0.5 x 6 x 50 = 3600 hours p.a.

Therefore, total number of hair salons = 40m hours / 3600 hours = 11,000 hair salons

Sense check: 11,000 salons implies 1 salon every ~700 people in NYC (350 men, 350 women). Given men cut their hair 12 times p.a. and women cut their hair 4 times p.a., that implies 5600 visits per year, or around 15-20 clients per day, which feels reasonable.

Note again that demand side estimation assumes there is a maximum efficient supply in the market, which may not be case.

Hope that is helpful!

Hi,

here's how I would approach it

- Define the geographic area to be covered [the whole world? the U.S.? NYC? Manhattan?...for this example I'll use Manhattan]

- Population living there [~ 1.5 M] + population travelling there for work or leisure [not sure about the figure, anything in the 50 - 100 M a year range]

- Divide the travellers figure per days of the year [100 M / 365 ≈ 275k]

- Assume a very low number of travellers comes to Manhattan by car [I'll say it's 0%] and most of the local population doesn't have / use the car [10% of people own a car and use it daily]

- The potential market for your service will be [275k] + [1.5 M * 90%] = [1.625 M]

- Assume [50%] of these people use public transportation, [20%] uses taxis and another [20%] either walks or bikes: this leaves you with [10% ~ 163k] potential daily customers

- Assume there's [10] competitors in this market with an equal market share: your company will process [10% of the transactions ~ 16k transactions a day]

All of the assumptions I used can obviously be challenged and can also be addressed by specific questions to the interviewer.

Hope this helped.

Best,

marco