[ajdecon]

i would never pass this test. i would solve this problem using variables for dimensions of the bus and a constant "packing factor" (or assume the optimal cannonball packing and approximate the golf balls as spheres) and write an express formula for the solution. then i would substitute in various constants for the dimensions and adjust the packing factor to find a range of solutions.

Oddly enough, this was exactly how I was taught to solve Fermi-like problems in my physics program. The point was not so much to be able to "intuit" the answer as to learn how to find approximate solutions with little or no real data. You could do this sometimes just with off-the-cuff estimates (as in the piano tuner example in https://en.wikipedia.org/wiki/Fermi_problem), but often enough we came up with approximate formulas and guessed at the constants.

I haven't been in enough startup job interviews to know if actually doing algebra would make them think less of me, but that would really seem pretty dumb.

[hedgie]

that may be an unfair assumption on my part. i just assumed that when people ask these abstract riddles, they're really looking for some way of testing your intuition and not something this mundane and boring.

it really boils down to basic algebra with some constant fudge factors. meanwhile, cs people have a host of sophisticated tools to estimate asymptotic behavior for the worst, best, and average case, or error bounds on solutions to NP complete problems as a function of the number of iterations of approximation algorithms, or trade-offs when certain pre and post conditions on the data influence the run-time of canonical algorithms (think searching).

the basic toolset of computer scientists is so advanced i guess i'm shocked anyone would ask such a relatively simple problem when there are much better ones out there.

[ajdecon]

Warning: I don't actually do web startups myself, so this is based on an outsider's view of the field.

Computer science provides some really awesome ways to deal with algorithmic problems... but for most startup-type applications, those problems only come into play in a few places (if that). A cool time-management webapp might have an interesting algorithm at its core that uses machine learning to auto-decide what tasks are most important (making something ridiculous up), but the rest of the app is basically just a shiny interface to a database.

I really doubt the problems of scaling a CRUD webapp (at less than Facebook scale) lend themselves to good mathematical analysis. Even if they did, these apps involve lots of third-party layers glued together to put together interesting functionality, and those seem to change often enough that it's not worth even trying detailed analysis.

So instead they do Fermi-problem estimates to figure out their basic scaling relationships. Then you can decide how to plug things together, decide what your basic resource constraints are (compute, memory, disk, bandwidth...) and make it easy to add those resources when your customer base expands.

Edit to add: Thinking a little more, that's exactly when you'd want a set of approximate algebraic constraints, so you could decide how many customers-per-EC2-instance you could serve and how that number might change as instance count increased. Math, it's important.

[hedgie]

that's a good point.

at my large company i do this every day on the embedded system i work on, which luckily is not a CRUD app. i guess i would hope they would ask me about that XD

databases can get tricky. but you're right, if something complicated like a bloom filter is used to solve subset-query it's probably in an third-party API they grabbed somewhere that handles most of the difficulty.