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Problem solving is like putting together a jigsaw puzzle. In the case of textbook problems, all the pieces are present and just need to be fitted together following the clues, and an possible a picture showing the desired result. In the case of real world problems, there may be missing pieces or extra pieces, and no guarantee that the solution can be done.

Novice problem solvers should examine:

- two logic puzzles
- chains of reason
- longer chains of reason
- islands and divisions of knowledge
- painless theorem proving

These appetizers and lessons show how rules and patterns may fit together to arrive at conclusions or solve SOME problems. Other problems are just too hard -- can't prevent that.

If your interest is in solving algebra word problems at the high school level, I would recommend learning how to solve linear equations in several unknowns in an effortless fashion. High school students who can solve linear equations in one unknown are often given word problems where extra variables have to be eliminated to formulate a single equation in one unknown quantity to solve. The trick here is to draw or extract a single equation from the given information. But in most such words problems, it is easier to extract or draw from the given information several linear equations in several unknowns to solve. Each sentence in the word problem gives an equation in one or more unknowns or quantities. Now the algebraic way of writing and thinking can be used to eliminate variables and to solve for the one or more quantities of interest in an effortless fashion.

The algebraic solution of linear equations involves the elimination of variables to obtain say one equation in one unknown. This elimination process may be better done and recorded with algebraic notation. Going directly to one equation in one unknown to solve a problem requires more work to be done with words.

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