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    <p>1 and 3 : Brute force means that <strong>you will go through all possible solutions extensively</strong>. For example, in a chess game, if you know you can win in two moves, the brute force will go through all possible combination of moves, without taking anything in consideration. So the little pawn in the back that cannot influence the outcome will still be considered.</p> <p>2 : As you consider everything, the problem quickly goes out of control. Brute force through 15 moves in chess is impossible because of combinatorial explosion (too many situations to consider). However, more clever algorithms that take into account "knowledge about the problem" can go much further (20-30 moves ahead) </p> <hr> <p>Edit : To clarify, <strong>brute force is simplest (dumbest?) way to explore the space of solutions</strong>. If you have a problem is set in a <a href="http://en.wikipedia.org/wiki/Countable">countable</a> space (chess moves are countable, passwords are countable, continuous stuff is uncountable) brute force will explore this space considering all solutions equally. In the chess example, you want to checkmate your opponent. This is done via a sequence of moves, which is countable. Brute force will go through all sequence of moves, however unlikely they may be. The word unlikely is important, because it means that if you have knowledge about your problem (you know what is unlikely to be the solution, like sacrificing your queen), you can do much better than brute force.</p>
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    1. POwhat exactly is the brute force algorithm
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    1. COso that because of combinatorial explosion means brute-force can not be used in many problems?
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    2. COThis is generally correct. The rule of thumb to know if it's possible to use brute force is to consider two things, the [branching factor](http://en.wikipedia.org/wiki/Branching_factor), and the depth at which you guess the solution is. Compute (branching factor) ^ (depth) and that's the number of situation brute force will consider. Most computers will not be able to consider 10^12 situations.
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    3. CO[Dynamic Programming](http://en.wikipedia.org/wiki/Dynamic_Programming) can sometimes help with exponentially complex problems.
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