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# How many trains are there in London?

brainteaser calculation estimation
New answer on Sep 06, 2019
3.0 k Views

I got this question during an interview for a non-consulting job before I learned at all about structuring and break-down analysis tecniques (so I was not prepared at all!). At the time I went down a "number of tube stations X number trains that pass in one day" path and ended up completely lost in a tangle of unnecessary calculations.

I'm curious to know how others would tackle this prolem.

• Date ascending
• Date descending
• Disclaimer: I'm no expert but this is how I would approach it.

1. Ask for or Estimate(pick a easy number to calc) the number of train routes in London

2. Assume average number of stations in a route - pick number

3. Assume average time between stations - this is also the frequency of trains at a station

4. State that for ease of calculation, you assume that at any point in time there is only train between 2 stations in any direction

5. No of trains = multiply Routes from 1 * (Avg No of stations -1) * Avg time taken between stations * 2

Multiple by 2 because train routes are bi directional

For extra point - say there would be a buffer of 10% for maintenance/peak times

or you can assume a certain percentage of routes are circular so you wont need to mutiply by 2