Manhattan sure has a lot of windows
06.26.2020 - Today's market sizing exercise
Hello Case Dojo,
We were feeling really tired today so we picked an online market sizing question instead of coming up with our own. It will only be original problems again after this, we promise. Good luck and have fun!
Reminders
Spell out your thinking process, state your assumptions, and evaluate your final answer. There are many valid approaches to each problem.
No calculators are allowed, so make the math easy for yourself.
Try to come to an answer within 3-4 minutes at the longest (here’s a timer).
Today’s Question
How many windows are there in Manhattan?
Assume Manhattan has 1.6M residents, 10 avenues, 200 streets, and covers a 23 square mile area.
Our sample answer
How we broke things down
This is a long one, so hang on tight.
If we find the number of buildings in manhattan and estimate the number of windows per building, we can multiply those two numbers to get the total windows.
Starting with the number of windows per building - let's separate buildings into 3 size classes: skyscraper, medium, and small. We can give an average number of floors per building in each class and the number of windows per floor to get an estimate for windows per building in each class.
We next take a weighted average of the windows per building in each class by the percentage of buildings in manhattan that are each class. This gets us the average windows per building.
The other big number we need - total buildings - comes from estimating the number of buildings on each block.
We can multiply by the number of blocks to get the total number of buildings and multiply with windows per building for our final answer
Assumptions we made
Skyscrapers on average have 60 floors and 40 windows per floor, midsize buildings have 20 floors and 25 windows per floor, and small buildings have 5 floors with 8 windows per floor.
Manhattan buildings are 20% skyscrapers and the rest evenly divided between midsize and small (40% each).
Each block has 10 buildings on each long side and 5 on each short side for 2 * 10 + 2 * 5 = 30 total buildings per block.
Our evaluation
We arrived at 46.2M windows. This feels like an overestimate for a few reasons: 1.) We do not account for the massive Central Park, which likely takes up a couple hundred blocks. 2.) A nontrivial number of blocks may be devoted to buildings without windows, such as parking lots and old banks.
Other potential approaches we like
Estimate the number of windows from the number of residencies plus the number of workspaces.
Estimate the total size of Manhattan and calculate windows per meter of street or something similar.
Actual answer
Go count them all yourself.
The New York Times says 4.6M windows, but then again, they also predicted Hillary Clinton would win the 2016 US Presidential election with 85% certainty.
Extras
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🤠 Fun Fact
It has become an economic rule that in NY, the cost of a subway ticket and a slice of pizza is the same.
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