I think this problem is a great interview question. It's easy to describe, and it's easy to get started solving it by writing the first few lines on the whiteboard. From there, the pattern should be obvious, and once you've recognized the pattern, you only need to write a few lines of code. The disadvantage is that someone might remember Pascal's triangle from high school math, and will try to "remember" the answer instead of actually solving the problem incrementally. This is worthless because the question is about problem solving ability rather than your memory of exam questions like "Expand (x+3)^27" or "Factor x^3 + 3x^2y + 3xy^2 + y^3". (I do remember writing Pascal's triangle on these sorts of exams, incidentally!)
Anyway, reading the other comments in the thread, it seems I am alone in liking this sort of question. I think these types of questions are good indicators of programmer quality. Anyone can read a Ruby on Rails tutorial and make an application that stores some records in a database. It doesn't take understanding to do that, it takes practice. That's all very good, as long as you're sure that your work will only be repeating what you've practiced rather than developing new skills. I think that programming work is very rarely like that. Yes, your job involves Ruby on Rails, but it's largely about solving some sort of complicated problem and then hooking the answer into your UI. Your experience with Rails will speed up the UI work, but if you aren't willing to understand and solve problems, you'll never have anything to put in the UI. (The people that can only do the UI part are "code monkeys" and don't get paid very well.)
If you think that you'll never need to understand problem X, it's simply because you are unwilling to understand problem X. Once you understand graphs and algorithms and data structures, you'll see how you can apply your understanding to write better software. You might not think they're very important, but that's because, right now, you have no idea of how those techniques might be important. Learn them and then come back and say "everything in CS class is garbage". You won't, because it's not. Your job will be easier and you won't be navigating the waters blind.
So I guess my point is: algorithm questions are good. There are a lot of programmers who can't solve problems (but can monkey code), and if you want the best programmers, you want the ones who can both solve problems AND write code.
Anyway, reading the other comments in the thread, it seems I am alone in liking this sort of question. I think these types of questions are good indicators of programmer quality. Anyone can read a Ruby on Rails tutorial and make an application that stores some records in a database. It doesn't take understanding to do that, it takes practice. That's all very good, as long as you're sure that your work will only be repeating what you've practiced rather than developing new skills. I think that programming work is very rarely like that. Yes, your job involves Ruby on Rails, but it's largely about solving some sort of complicated problem and then hooking the answer into your UI. Your experience with Rails will speed up the UI work, but if you aren't willing to understand and solve problems, you'll never have anything to put in the UI. (The people that can only do the UI part are "code monkeys" and don't get paid very well.)
If you think that you'll never need to understand problem X, it's simply because you are unwilling to understand problem X. Once you understand graphs and algorithms and data structures, you'll see how you can apply your understanding to write better software. You might not think they're very important, but that's because, right now, you have no idea of how those techniques might be important. Learn them and then come back and say "everything in CS class is garbage". You won't, because it's not. Your job will be easier and you won't be navigating the waters blind.
So I guess my point is: algorithm questions are good. There are a lot of programmers who can't solve problems (but can monkey code), and if you want the best programmers, you want the ones who can both solve problems AND write code.