Rectangle Counting Tricks

Duration: 9 min

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Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Ability: Speed Mathematics and Basic Mathematics, Percentage, Ratio and Proportion (Ratios), Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Pipe and Cistern, Speed Time and Distance, Number System, HCF LCM, Data Interpretation, Age Problems, Mixture and Alligation, Partnership, Algebra, Sequence and Series (Series), Mensuration and Geometry, Arithmetic
  2. Reasoning Ability: Puzzle Solving (Puzzles), Seating Arrangements, Coding Decoding, Blood Relations, Directions (Direction Test), Syllogisms, Data Sufficiency, Ranking, Order and Sequence, Series (Number and Letter Series) (Numerical Relations and Reasoning), Logical Sequence Of Words, Calendar, Clock, Cubes & Dices, Analytical Reasoning (Counting Figures Reasoning), Data Arrangement, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning)
  3. Verbal Ability: Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Vocabulary, Sentence Completion (Fill in the blanks), Active Passive Voice (Voice), Direct and Indirect Speech, Subject Verb Agreement (Verb Noun Agreement), Tenses, Preposition, Articles, Sentence Correction (Error Correction)
  4. Programming Basics (MCQs + Interview): C Programming by Yash Sir, Programming in C++, Java, Python for Placements by Yash Sir
  5. OOPs (MCQs + Interview): Object Oriented Programming (OOPS)
  6. DBMS (MCQs + Interview): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Transaction Management, Decomposition Properties & 4NF, Concurrency Control, Database Recovery, File Organization & Indexing, Relational Algebra, Database Security & Authorization
  7. SQL (MCQs + Interview): SQL
  8. Operating Systems (MCQs + Interview): Introduction to OS, Process Management, CPU Scheduling, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Process Synchronization, Disc Scheduling, File Management, Security
  9. Computer Networks (MCQs + Interview): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security, Mobile Technology, Cloud Computing and IoT, Cyber and Info Security
  10. Coding: Coding Questions by Yash Sir
  11. HR Interview: MR & HR Interview Preparation
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This video is a tutorial on counting rectangles in a grid, presented by an instructor named Yash Jain. The lesson begins with a 3x3 grid, where the instructor demonstrates a method to count all possible rectangles by summing the number of rectangles of each size. He explains that the total count is the product of the sum of the first n natural numbers for the rows and the sum for the columns. For a 3x3 grid, this is (1+2+3) * (1+2+3) = 6 * 6 = 36. The instructor then extends this concept to a 4x4 grid, showing the calculation as (1+2+3+4) * (1+2+3+4) = 10 * 10 = 100. The video uses a whiteboard to illustrate the method, writing out the sums and the final multiplication. The core idea is that for an n x n grid, the total number of rectangles is [n(n+1)/2]^2. The video concludes with a thank you message.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title card reading "RECTANGLE COUNTING TRICKS". The scene then transitions to a classroom setting where an instructor, identified as Yash Jain Sir, stands in front of a whiteboard. On the board, a 3x3 grid is drawn. The instructor begins to explain the problem of counting all the rectangles within this grid, setting up the lesson. The on-screen text identifies the instructor as a Knowledge Gate Educator and promotes a placement preparation course.

  2. 2:00 – 5:00 02:00-05:00

    The instructor demonstrates the method for counting rectangles in the 3x3 grid. He writes the sum of the first 3 natural numbers, 1+2+3, and calculates it to be 6. He then explains that this sum represents the number of ways to choose a vertical line for the rectangle's width. He repeats this for the horizontal lines, writing 1+2+3=6. He then multiplies these two sums, writing 6 x 6 = 36, to find the total number of rectangles. He explains that this method works because any rectangle is defined by choosing two vertical lines and two horizontal lines from the grid.

  3. 5:00 – 8:46 05:00-08:46

    The instructor moves on to a 4x4 grid, drawing it on the whiteboard. He applies the same method, writing the sum 1+2+3+4 and calculating it to be 10. He then multiplies 10 by 10, writing 10 x 10 = 100, to find the total number of rectangles in the 4x4 grid. He explains that the formula for an n x n grid is [n(n+1)/2]^2. The video ends with a "THANKS FOR WATCHING" screen.

The video provides a clear, step-by-step demonstration of a mathematical trick for counting rectangles in a grid. It starts with a simple 3x3 grid, breaking down the counting process into the sum of natural numbers for rows and columns, and then multiplying the results. The instructor then applies this same logic to a 4x4 grid, reinforcing the concept. The core of the lesson is the formula for the total number of rectangles in an n x n grid, which is derived from the sum of the first n natural numbers, a fundamental concept in combinatorics.

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