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For a given
problem, you might want to try these suggestions.
- Read and understand the problem and what is
asked.
- Convert the problem statement into an
equivalent equation or set of equations. If you have
N unknowns,
then you will need N
linearly independent equations to solve.
- Draw a picture to help visualize the problem
and understand what is being asked. Drawing a chart
or diagram could help in many cases.
- Replace names with letters in your
expressions.
- Guess and check. This is not a great
strategy, but can work sometimes. When checking your
guess, make sure it is consistent with all parts of
the problem statement.
- Use algebra. Unfortunately, this implies that
you know algebra. Many problems are much easier if
you can apply some very basic algebraic concepts
like solving an equation that has an unknown or
solving N equations with N unknowns.
- Don't be sloppy when you work it out on
scratch paper. Be neat and organized.
- Watch out for traps. Sometimes
the most obvious answer is not the right one. Recall
the problem with Peter, Tommy, and Vince who did not
respectively play the piano, trumpet, and violin.
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