Rectangle Counting Tricks

Duration: 9 min

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Inside: a video lesson and guided study material.

Module outline

  1. Communication Round: Vocabulary, Subject Verb Agreement (Verb Noun Agreement), Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Direct and Indirect Speech, Active Passive Voice (Voice), Verbal Analogy (Word Based Analogy), Articles, Preposition, Conjunction, Sentence Construction, English Writing Ability, Communication Assessment
  2. Quantitative Aptitude: Ratio and Proportion (Ratios), Divisibility Rules, Data Interpretation, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Speed Time and Distance, Percentage, Average, Powers and Exponents (Surds and Indices), Time and Work, Mensuration and Geometry, Age Problems, Pipe and Cistern, Probability, Profit and Loss, Simple Interest and Compound Interest, Algebra
  3. Analytical and Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Directions (Direction Test), Ranking, Order and Sequence, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Logical Sequence Of Words, Puzzle Solving (Puzzles), Syllogisms, Seating Arrangements, Calendar, Clock, Blood Relations, Cubes & Dices, Venn Diagram, Analytical Reasoning (Counting Figures Reasoning)
  4. Cognizant Gaming Aptitude: Gamified / Game Based Aptitude
  5. Java (Cluster 1): Java
  6. ANSI SQL MySQL (Cluster 1,2,3): SQL
  7. HTML, CSS, JavaScript (Cluster 1,3): HTML, CSS, JavaScript
  8. Python (Cluster 2): Python for Placements by Yash Sir
  9. Cloud Fundamentals (Cluster 2): Emerging Tech Trends
  10. C# (Cluster 3): C#
  11. OOPs: Object Oriented Programming (OOPS)
  12. Technical Assessment (Coding): Coding Questions by Yash Sir, C Programming by Yash Sir, Programming in C++, Pseudo Codes
  13. Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  15. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  16. Computer Networks: 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
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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