Description FACTO (Free Active Creative Thinking O. Junior Mathtian) is a junior mathematician who thinks freely, confidently, and creatively. This book is a creative-thinking math exploration workbook designed for advanced-level students. It presents representative problem types across 180 key creative-thinking topics, organized by area, allowing students to build problem-solving skills and deeper thinking abilities. It also serves as an advanced creative-thinking preparation resource for various domestic and international math competitions, as well as gifted education programs run by universities and regional offices of education. 1) Organized by Representative Creative-Thinking Topics at Each Level Each level is thoughtfully composed of representative creative-thinking topics, allowing students to explore various approaches and dig deeply into different problem types. By presenting representative problem types for each major creative-thinking theme, students can understand core principles and systematically approach problems by following the flow of their reasoning. 2) Problem-Type Analysis for Gifted Classes, Gifted Education Centers, and Competitions With the growing number of students eligible for gifted education, this book is composed of representative problem types that frequently appear on gifted education center entrance exams, helping students gradually prepare for gifted classes and gifted education centers. 3) Rich and Thorough Manual The manual provides detailed explanations for each problem and highlights key points at a glance. Rather than simply solving problems and checking answers, students can study effectively and independently without missing important concepts. 4) Diagnostic and Comprehensive Assessments Provided A diagnostic assessment available through the Mathtian website (http://www.mathtian.com) helps determine the appropriate level of the workbook for each student, and a comprehensive assessment after completing the book helps check overall achievement. 5) Online Services Provided Through the Naver Cafe (http://cafe.naver.com/factos.cafe), a variety of creative-thinking resources and learning information are continuously provided, including preschool and elementary math learning methods, past gifted education center exam questions, practice questions, video lectures, and Q&A. I. Number Sense 1. Various Multiplication Methods 2. Sums That Cannot Be Made 3. Sums of Numbers Made from Number Cards 4. Maximum and Minimum of Products, Quotients, and Remainders 5. Four Fours (Four 4s) 6. Cryptarithms and Missing Digit Problems II. Puzzles and Games 1. Sudoku 2. The Principle of Magic Squares 3. Various Nim Games 4. Polyominoes 5. Pentominoes 6. Dividing Shapes III. Geometry 1. Nets of a Rectangular Prism Without a Lid 2. Nets of a Rectangular Prism 3. Cross-Sections of a Cube 4. Coloring and Cutting a Cube 5. Combining Cubes 6. Soma Cube IV. Finding Patterns 1. Number Sequences 2 2. Patterns in Arrangement 3. Patterns in Shapes 4. Patterns in the Number of Shapes 5. Rules 1 6. Pascal's Triangle V. Measuring Shapes 1. Perimeter of a Rectangle 2. Perimeter of Combined Shapes 3. Area of a Lawn 4. Unit Area 5. Area of Overlapping Shapes 6. Dividing Area in Half VI. Number Theory 1. Ancient Numbers 2 2. Making Numbers and Counting Them 3. Sum of Digits 4. Number of Digits and Numbers 5. Divisibility Rules 6. Counting Each Digit VII. Logical Reasoning 1. Arranging Numbers 2. Deductive Logic 1 3. Truths and Lies 4. Tiling with Dominoes 5. The Bridges of Königsberg 6. The Pigeonhole Principle 2 VIII. Spatial Sense 1. The Seven-Point Principle of a Die 2. Viewing a Die from Three Sides 3. Nets of a Die 4. Transparent Solid Shapes 5. Various Nets 6. Applying Nets IX. Counting 1. Number of Shortest Paths 2 2. Number of Possible Routes 3. The Frobenius Coin Problem 4. Lining Up 5. Selecting Representatives 6. The Worst-Case Scenario X. Problem-Solving Skills 1. Age Calculations 2. Calendar Problems 3. Optimal Planning 4. Measurable Lengths and Weights 5. Applying Sequences 6. The Tower of Hanoi