How do you answer 'Describe a time you solved a problem' in a job interview?

Answer

If you're not the supervisor or in management, you have no business making business decisions. It's a trick question.
What they want to know is how you delegated problems to the proper channels. They want to know If you contacted your higher-ups with the present dilemna and gave them a briefing on the situation.
What you want to do is get the name of the person who has the problem, and his/her phone number. Call your supervisor and if he/she isn't there, leave a message about the situation and give the person's name and number. The customer will have to be patient because there's nothing you can do.
You tell your co-workers about the situation, and let the next shift be aware of the situation as well. It's all about communication and delegation of authority in business. If you were hired to solve problems, then of course, tell them of your problem solving skills.  

Every employee solves problems...

Let's say you're a retail associate and you sell faucets. A customer wants a faucet that's on display. You're completely out of them. A good way to solve the problem would be to call another store that has some and get one sent to you. You wouldn't delegate that problem to a "proper channel" because YOU are the proper channel.
Agreed - This is not a trick question. Basically, the interviewer wants to get an idea of your judgment and decision making skills as well as what factors you considered in your decision and whether or not you involved or consulted others. More and more, companies are looking for critical thinkers who use good judgment both for the Customer and the company.