2018_Solutions_Grades 9-10-2018_Solutions_Levels

2018_Solutions_Levels_9&10

Pdf Summary

The Mathematics Kangaroo 2018 competition for Levels 9-10 challenged participants with a variety of problems. Here are some key solutions and insights into these problems:<br /><br />1. **Number of Children**: Given each boy in a family has at least two brothers and each girl at least one sister, the minimum number of children is five.<br /><br />2. **Triangle Inequality**: To find the length of a third side that must be an integer and odd, the only suitable length is 5.<br /><br />3. **Table Height**: By solving two related equations, the height of a table is calculated to be 130 cm.<br /><br />4. **Hexagon Area**: In a regular hexagon, each triangle formed by connecting the center and two adjacent vertices is congruent; hence, shaded and unshaded areas are equal.<br /><br />5. **Bus Stop Problem**: The optimal position for a bus stop minimizes total walking distance and is directly in front of the second building.<br /><br />6. **Solution and Logic**: The paper delves deep into geometric and number sequence problems, using logical deductions and arithmetic calculations.<br /><br />7. **Complex Counting and Geometry**: Problems involving counting paths between points, computing areas, or determining number properties highlight the necessity for both spatial reasoning and algebraic skills.<br /><br />8. **Integer Solutions**: Participants demonstrated skill in deducing likely solutions via inequalities and integer constraints.<br /><br />9. **Pattern Recognition**: Problems required identifying and proving patterns in sequences and arrangements.<br /><br />Through these illustrations, the competition exemplified that careful reasoning, a good grasp of geometric properties, mathematical proofs, and pattern identification are crucial for problem solving at this level. Each solution focused on elegance and simplicity, often revealing hidden efficiencies or logical insights critical for determining the correct answer.

Keywords

Mathematics Kangaroo

competition

problem solving

geometric properties

pattern recognition

integer solutions

triangle inequality

hexagon area

bus stop problem

logical deductions