Also worth asking, are you willing to learn 2000+ year old greek to read Euclid or for Euler learn Latin (the language in of scholarship in his time)? One reason that we have and use more modern math textbooks is changes in language and notation over time. Also it is often the case that the original proof is far from the best that has been found since there is now more structure developed in later works that allows either condensing or a novel approach. If you limit yourself to pre-1900 works, you throw out the vast majority of Graph Theory losing all contributions by Erdos, Kuratowski, Tutte, Ramsey, etc. Sorry, there are areas of math that need at least up to the 1950's to get major theorems.
I am from the opposite end of things, someone who did math competitions from elementary through undergrad and who misses having them in graduate school. That said,
The Art of Problem Solving books might work for you. They are intended to help students prepare for middle and high school math competitions, have solution manuals, and are $73 for both books and their solution manuals. There is also a new strictly algebra book available. My main reason for recommending this is that the whole point of most math competitions and these books is to teach you problem solving techniques, you will learn algebra, geometry, trig, etc, but also learn more of how to apply them to more interesting/applicable problems.
http://www.artofproblemsolving.com/
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Also worth asking, are you willing to learn 2000+ year old greek to read Euclid or for Euler learn Latin (the language in of scholarship in his time)? One reason that we have and use more modern math textbooks is changes in language and notation over time. Also it is often the case that the original proof is far from the best that has been found since there is now more structure developed in later works that allows either condensing or a novel approach. If you limit yourself to pre-1900 works, you throw out the vast majority of Graph Theory losing all contributions by Erdos, Kuratowski, Tutte, Ramsey, etc. Sorry, there are areas of math that need at least up to the 1950's to get major theorems.
I seem to recall that most bike locks have a "void in NYC" warranty.
I am from the opposite end of things, someone who did math competitions from elementary through undergrad and who misses having them in graduate school. That said, The Art of Problem Solving books might work for you. They are intended to help students prepare for middle and high school math competitions, have solution manuals, and are $73 for both books and their solution manuals. There is also a new strictly algebra book available. My main reason for recommending this is that the whole point of most math competitions and these books is to teach you problem solving techniques, you will learn algebra, geometry, trig, etc, but also learn more of how to apply them to more interesting/applicable problems. http://www.artofproblemsolving.com/