- Technical knowledge of specific technology product
- Experience of the business problem domain
- General technical and architecture sense
- Personality and working style
- IQ, problem solving skills

I personally believe that a short interview doesn't necessary reflects a person's ability in doing the actual work. I personally have worked with many people who is a high performer in work but a poor interviewee. So don't lose confidence because you fail an interview, there is a factor of luck involved in this process.

Nevertheless, most employers are willing to accept a higher false negative, but the chance of false positive must be very low. Because the pass rate of these IQ and algorithm questions are generally pretty low, it is a very effective means of filtering the candidates. Therefore, be able to tackle this kinds of question well is a critical success factor of interviewing.

Notice that there is no substitution of "good knowledge", "high IQ" and "the ability to speak/think under a pressured environment", but I've found there are some very useful technique and strategies.

1. Rephrase the question slowly in your own words

This can help you to make sure you fully understand the question and clarify if there is any hidden assumptions you have made. Repeat the question "slowly" also gives you more time to think.

From the interview perspective, he/she can see clearly the candidate's ability to digest a problem.

2. Construct a Visual model of the problem

Use a whiteboard, or paper (if this is a phone interview) to diagram the problem that you perceive. Our brain is good in understanding picture than words so having a diagram will be very useful to come up with solution ideas.

From an interview's perspective, he/she can see a clear picture how you analyze the problem.

3. Use a special, simple case to guide you

Never try to tackle the general problem at first, start with a super-simple, special case, and think how you would solve this simple case first. This is very helpful to reduce the amount of things that you need to consider and let you focus in the core part of the problem.

4. Start with a very naive solution as a baseline

Tell the interviewer that you want to start with a very naive solution to establish a baseline. The naive solution can usually be constructed using a brute-force approach (try all combination until you find a matched solution). After that analyze the complexity of this naive solution as a baseline for future comparison.

5. Improve your solution

At this stage, you need to evolve and improve your solution. Here are some general techniques.

- Divide and conquer: Decompose the problem into smaller ones and solve each sub-problem separately, then combine the solutions for the overall problem.
- Reduce to well-known algorithm models: Try to model your problem in terms of well-studied computer science data structure model (e.g. Tree, Graph, Search, Sort) and then apply well known algorithm to solve them
- Recursive structure: Try to structure your problem in a recursive form. Finding the solution for the base case and then expand the solution in a recursive manner.
- Greedy method: Try to modify attributes of your current best solution to see if you can get a better one. Watch out of being trapped in a local optimal solution.
- Approximation: Instead of finding an exact solution, try to see if it is acceptable to find an approximate solution. Probabilistic approach (try 100 random combination and pick the best outcome)

Don't wait until you fully figure out the answer. Keep talking while you are thinking about the solution so the interviewer understand how you analyzing things, and you are also showing how well you can express your thoughts. It is also easier for the interviewer to guide you or give you hints. And finally you may impressed the interviewer even you cannot get to the exact answer.

7. Generalize your solution for the final answer

After you find a working solution for the simple case, extend the simple case to see how you would solve it. See if you can find a general pattern how the solution would look like. Once you find it, generalize your solution for the general problem

From the interview's perspective, he/she can assess if the candidate can think in different levels of abstraction, and the ability to apply a solution in a broader scope of problem.

8. Remember the interview hasn't ended at the office building

You always have the chance to think through the question that you haven't given satisfactory answer after you walk out from the office. Submit a solution via email once you get back home (do it ASAP though), along with a thank you note to the interviewer.