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The second edition of this book is out! Please look for the second edition updated and improved! This is the first edition. About "Competitive Mathematics for Gifted Students" This series provides practice materials and short theory reminders for students who aim to excel at problem solving. Material is introduced in a structured manner: each new concept is followed by a problem set that explores the content in detail. Each book ends with a problem set that reviews both concepts presented in the current volume and related topics from previous volumes. The series forms a learning continuum that explores strategies specific to competitive mathematics in depth and breadth. Full solutions explain both reasoning and execution. Often, several solutions are contrasted. The problem selection emphasizes comprehension, critical thinking, observation, and avoiding repetitive and mechanical procedures. Ready to participate in a math competition such as MOEMS, Math Kangaroo in USA, or Noetic Math? This series will open the doors to consistent performance. About Level 1 This level of the series is designed for students who know addition and subtraction with multi-digit numbers as well as simple multiplications of one-digit numbers. Some of the problems, however, involve advanced concepts and may be useful for older students. About Volume 2 - Observation and Logic The problems in this volume are based on contrast, surprise elements, and lateral thinking. They encourage students to give themselves more freedom in exploring the universe of each problem statement. Creative thinking is rewarded, but repetitive thinking is not. Advanced mathematical concepts are introduced in simplified forms. This book includes patterning and an elementary treatment of rates.