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How can we solve these problems withing using brute force?

http://edhelper.com/math/multiplication51.htm

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    What is brute force? Is it using logic to reduce the number of possible cases, then testing those?2011-11-03
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    It also looks like they are intended for 5th graders. I'm working on applying some logic to it now. Brute force would be writing a computer program in order to solve this or (shudder) manually trying every combination. I think we can do better..2011-11-03
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    this can be done by applying systems of equations with several variables2011-11-03
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    pedja, how? can you show an example?2011-11-03
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    These are known as "cryptarithms" or "verbal arithmetic". You can get started in [Wikipedia's page on solving them](http://en.wikipedia.org/wiki/Verbal_arithmetic). As the page notes, one usually uses a mix of logic to eliminate possibilities and reduce to a small number, and then a bit of trial-and-error.2011-11-03

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