Problem Solver's Toolbox: Difference between revisions

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== General ideas ==
== General ideas ==


Should we add some general problem solving ideas here? (E.g. like this: [https://en.wikipedia.org/wiki/How_to_Solve_It]).
Should we add some general problem solving ideas here? (E.g. like this: [https://en.wikipedia.org/wiki/How_to_Solve_It How to Solve It]).





Revision as of 17:01, 26 November 2016

This will be a page for the Wisconsin Math Talent Search where we will collect simple problem solving strategies.


General ideas

Should we add some general problem solving ideas here? (E.g. like this: How to Solve It).


Modular arithmetic

When we have divide two integers, they don't always divide evenly, and there is a quotient and a remainder. For example when we divide 10 by 3 we get a remainder of 1. It turns out that these remainders behave very well under addition, subtraction, and multiplication. We say two numbers are the same "modulo m" if they have the same remainder when divided by m. If a and a' are the same modulo m, and b and b' are the same modulo m, then a+b and a'+b' are the same modulo m, and similarly for subtraction and multiplication. This often makes calculation much simpler. For example, see 2016-17 Set #2 problem 3.

See Art of Problem Solving's introduction to modular arithmetic for more information.


Mathematical induction

Angles in the circle