Lesson Plans SET A for Grades 9-10-Lesson 4 Logical Reasoning Homework Solutions

Lesson 4 Logical Reasoning Homework Solutions

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The document contains solutions to a logical reasoning homework set aimed at students at levels 9-10. It comprises five different problems, each addressing distinct logical puzzles or reasoning issues.<br /><br />1. **Dice Faces Problem**: It involves deducing opposite faces of a cube based on shared edges. Faces opposite each other are identified through edge-sharing logic, revealing that one configuration results in the visible sum of faces from a specific view equaling 13.<br /><br />2. **Perfect Square Ages Problem**: This problem deals with determining the ages of four individuals based on conditions involving square numbers. Through analysis and trial-and-error, two numbers remain perfect squares after subtracting 15, revealing ages as 16, 24, 25, and 64.<br /><br />3. **Counterfeit Coin Problem**: This challenge requires identifying a counterfeit coin in one of four piles. By using a sequence of weighings and applying balancing techniques, the counterfeit coin—whether lighter or heavier—is found through division into smaller piles, culminating in a simple weight comparison.<br /><br />4. **Hexagon Coloring Problem**: The task involves determining a monochrome triangle within a hexagon whose sides and some diagonals are colored in two colors. Using the pigeonhole principle, it's concluded that there must always be a triangle with all sides of the same color.<br /><br />5. **Logical Deduction Problems**: Three scenarios are provided, analyzing premises via diagrams to determine argument validity:<br />   - Scenario (a) uses disjoint sets to establish a valid argument.<br />   - Scenario (b) shows an invalid argument due to the lack of necessary intersections.<br />   - Scenario (c) involves categorizing books, demonstrating that all adventure books are well-written, yielding a valid argument.<br /><br />Each section requires logical thinking and applying principles to reach the solutions provided.

Keywords

logical reasoning

dice faces

perfect square ages

counterfeit coin

hexagon coloring

pigeonhole principle

logical deduction

valid argument

disjoint sets

well-written books