There are more option than the following scenarios:
(1-3). Know the solution already or be a genius and find the solution surprisingly fast.
4. Sit there feeling stupid.
The idea is to give you an extraordinarily hard problem without the expectation that you'll solve it. The reasoning of the employer is the following:
I. You fall into the options (1-3) and you are either a genius or the question was too easy. Either way its not bad for you.
II. You don't have enough knowledge at hand to approach the problem. Then you do either what described in option 4. xor you accept and be honest when you don't know something and you know what to do next; identify information you are missing and how you can get it.
Since the case I. is rare and the case II. gives the employer a good picture of you it's a good question for an interview.
(1-3). Know the solution already or be a genius and find the solution surprisingly fast.
4. Sit there feeling stupid.
The idea is to give you an extraordinarily hard problem without the expectation that you'll solve it. The reasoning of the employer is the following:
I. You fall into the options (1-3) and you are either a genius or the question was too easy. Either way its not bad for you.
II. You don't have enough knowledge at hand to approach the problem. Then you do either what described in option 4. xor you accept and be honest when you don't know something and you know what to do next; identify information you are missing and how you can get it.
Since the case I. is rare and the case II. gives the employer a good picture of you it's a good question for an interview.