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Research the art and craft of problem

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Research:  The Art and Craft of  Problem Solving (ACPS) Types of Problems Recreational Contest Journal Open-Ended Exercises and Problems
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ACPS : An Analogy The  average  (non-problem-solver)  math  student  is  like  someone  who  goes to a gym three times a week to do lots of repetitions with low  weights on various exercise machines. In contrast, the problem solver  goes on a long, hard backpacking trip. Both people get stronger. The  problem  solver  gets  hot,  cold,  wet,  tired,  and  hungry.  The  problem  solver gets lost, and has to find his or her way. The problem solver  gets blisters. The problem solver climbs to the top of mountains, sees  hitherto undreamed of vistas. The problem solver arrives at places of  amazing  beauty,  and  experiences  ecstasy  that  is  amplified  by  the  effort expended to get there. When the problem solver returns home,  he  or  she  is  energized  by  the  adventure,  and  cannot  stop  gushing  about the wonderful experience. Meanwhile, the gym rat has gotten  steadily  stronger,  but  has  not  had  much  fun,  and  has  little  to  share  with others (page x).
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Research:  ACPS Problem solving is learned.  History There is no wrong path. It has a definite structure. Strategies Tactics Tools
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Strategies Tactics Tools Bend the Rules* Extreme Principle* Factor* Penultimate Step Pigeonhole Principle Add Zero Creatively Get Your Hands Dirty* Invariants Invent a Font Restate the Problem Symmetry* AM-GM Obtain Partial Solution Substitution* Massage Inequalities Change Point of View Modular Arithmetic* Telescoping Series
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Research:  ACPS  (Uniqueness) Emphasis should be placed more on exploration than  presentation.
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