Webinars SET A - Grade 7-8 - Sunday@3:15-4:15pm EST-Recording Webinar 9

Video Transcription

Video Summary

The session begins with a warm-up logic puzzle involving Ada’s bag of colored balls, emphasizing worst-case scenario reasoning to ensure drawing at least one ball of each color. The instructor introduces key problem-solving strategies: planning, careful calculation, and validation of answers, highlighting the importance of logic as a branch of math grounded in reasoning.<br /><br />Core concepts covered include deductive reasoning, the pigeonhole principle illustrated with matching socks, cryptarithms (letter-substituted arithmetic puzzles), and knights and knaves problems involving truth-tellers and liars. Logic puzzles requiring deduction via elimination and charting are also explained, with examples for practice.<br /><br />Several practice questions from past competitions are then explored in detail:<br /><br />1. Height comparisons among friends using inequalities and charts, concluding the correct comparative statement.<br />2. A problem on guaranteeing consecutive sunny days at a Caribbean hotel using worst-case reasoning and the pigeonhole principle, concluding a minimum stay of 32 days.<br />3. A complex counters problem involving color distributions solved by setting inequalities and summing constraints, yielding a maximum of 29 counters.<br />4. A multiplication puzzle with missing digits, solved through logical trial, identifying the digits scribbled out sum to six.<br />5. A cryptarithm involving letter-based multiplication and showing that zero as a digit leads to a unique product, confirming only one possible product value.<br />6. A letter-digit puzzle to find the largest sum in a cryptarithm-based addition, solved through digit elimination and logical deduction, concluding the largest possible sum is 9873.<br /><br />Throughout, the instructor encourages reasoning through worst-case scenarios, organizing information with tables, and continuous critical thinking. The session ends with an invitation for questions, commending participants for their problem-solving progress.

Keywords

logic puzzles

worst-case scenario

deductive reasoning

pigeonhole principle

cryptarithms

knights and knaves

inequalities

logical deduction

problem-solving strategies

critical thinking