that formula narrows it down pretty well once the constants are defined and takes about a minute to determine. with more time than is found in a typical job interview you could actually go much further.
the real criticism of the question is that the real skill they're trying to test is better determined by directly asking about Fermi calculations relating to computer software and hardware.
the golf ball question could be interesting in it's own right, but it's asked in a context where additional information to optimize the solution is not available and an optimized solution couldn't be determined due to time constraints. hence the formula sucks and you end up simplifying it with fudge factors that only demonstrate that you are able to use basic algebra to model the volume of a bus and a golf ball.
there are numerous practical reasons you would want to solve this problem. for example, say you work in an orange factory. you want to pack oranges of radius n. perhaps you would like to determine and minimize the amount of shrink wrap you have to stretch around them for transport, or keep track of the materials cost for accounting purposes.
that's essentially the same problem and uses the same formula, you're just solving for the dimensions of the container instead of the number of golf balls. you can save a lot of money minimizing the wrapping material if you pump out hundreds/thousands of packed oranges a day and choose an optimal packing.
alternatively, if you have to ship it in a non-optimal packing like boxes, perhaps it's good to calculate the materials cost to pack your product to estimate future expenses.
that article lists other problems where sphere packing is integral to the solution. just because an application doesn't seem obvious doesn't mean there isn't one.
if someone honestly expected me to challenge this interview question without understanding how it could be useful i would rather not work there. people have been studying this problem for practical reasons ever since they had to stack cannonballs for transport, it's not exactly a contrived example.
I understand the value of sphere packing (but IMHO ellipsoid packing is more interesting), but why not just ask the orange packing question instead of golf balls on a bus?
A question about orange packing in an orange factory simply does not elicit the reaction of "let's see if this monkey can dance" which one would have if asked about golf balls on a bus.
An intentionally absurd question, even if it is an abstraction of a non-absurd question, does not make that question any less absurd. If you want to abstract, abstract, but do not abstract then unproductively obfuscate, because when you do, you've taken a perfectly legitimate problem and made a trick question out of it.
the real criticism of the question is that the real skill they're trying to test is better determined by directly asking about Fermi calculations relating to computer software and hardware.
the golf ball question could be interesting in it's own right, but it's asked in a context where additional information to optimize the solution is not available and an optimized solution couldn't be determined due to time constraints. hence the formula sucks and you end up simplifying it with fudge factors that only demonstrate that you are able to use basic algebra to model the volume of a bus and a golf ball.
see:
http://en.wikipedia.org/wiki/Sphere_packing
there are numerous practical reasons you would want to solve this problem. for example, say you work in an orange factory. you want to pack oranges of radius n. perhaps you would like to determine and minimize the amount of shrink wrap you have to stretch around them for transport, or keep track of the materials cost for accounting purposes.
that's essentially the same problem and uses the same formula, you're just solving for the dimensions of the container instead of the number of golf balls. you can save a lot of money minimizing the wrapping material if you pump out hundreds/thousands of packed oranges a day and choose an optimal packing.
alternatively, if you have to ship it in a non-optimal packing like boxes, perhaps it's good to calculate the materials cost to pack your product to estimate future expenses.
that article lists other problems where sphere packing is integral to the solution. just because an application doesn't seem obvious doesn't mean there isn't one.
if someone honestly expected me to challenge this interview question without understanding how it could be useful i would rather not work there. people have been studying this problem for practical reasons ever since they had to stack cannonballs for transport, it's not exactly a contrived example.