Rectangle Counting Tricks

Duration: 9 min

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Inside: a video lesson and guided study material.

Module outline

  1. Paper 1 | Reasoning Test: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Seating Arrangements, Blood Relations, Puzzle Solving (Puzzles), Venn Diagram, Analogy, Ranking, Order and Sequence, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Selection Decision Table (Decision Making), Logical Sequence Of Words, Cubes & Dices, Analytical Reasoning (Counting Figures Reasoning), Calendar, Alphabet and Word Tests, Numerical Reasoning, Number System, Averages, Mixtures and Alligation, Percentages, Series Completion, Analogy and Classification, Patterns in Two-Dimensional Figures, Coding and Decoding, Mathematical Operations, Direction Sense, Algebra, Logical Deduction and Induction, Syllogisms and Venn Diagrams, Critical Reasoning, Order, Ranking and Sequence, Reading Comprehension, Profit, Loss and Discount, Constraint Puzzles, Speed, Time and Distance, Traverse Surveying, Ratio and Proportion, Time and Work, Mensuration, Permutations and Combinations, Clocks and Calendars, Data Interpretation, Assembling and Grouping of Shapes, Transformation of Shapes, Three-Dimensional Patterns and Visualization, Cubes and Dice, Vocabulary, Blood Relations, Data Sufficiency
  2. Paper 1 | Numerical Analysis: Number System, HCF LCM, Percentage, Ratio and Proportion (Ratios), Average, Sequence and Series (Series), Powers and Exponents (Surds and Indices), Algebra, Statistics, Data Interpretation, Mental Ability, Arithmetic, Logarithm, Profit and Loss, Simple Interest and Compound Interest, Speed Time and Distance, Mixture and Alligation, Mensuration and Geometry, Permutation and Combination, Probability, Sequences and Series, Powers, Surds and Logarithms, Subject-Verb Agreement, Sentence Completion, Geometry, Sentence Structure and Correction, Data Sufficiency, Trigonometry, Measurement and Quantity Take-Off, Signal Space and Optimum Detection, Probability, Statistics, Algebra, Time and Work, Speed, Time and Distance, Data Interpretation, Graph Theory, Combinatorics
  3. Paper 1 | General Knowledge: State Wise GK, History, Geography, GK- Current Affairs, Static General Knowledge, Polity, Indian Economy
  4. Paper 1 | DBMS: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Transaction Management, Concurrency Control, Relational Calculus, Database Security & Authorization, Database Recovery
  5. Paper 1 | Data Communication & Network: 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, Network Security, Security in Mobile and Wireless Computing, Input Output Organisation, File Management, Hardware Basics, Terms & Abbreviations, Protocols & Services, Network Access Technologies, Cyber Safety and Security, Basics of COA
  6. Paper 2 | System Analysis & Design: Fundamentals of Systems and Information Systems, SDLC and Development Approaches, Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Documentation and Software Requirements Specification (SRS), SDD and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Security, Risk Management & Maintenance, extras
  7. Paper 2 | Programming Language (Java): Java Fundamentals, OOPS with Java, Array, String, IO & References, Generic & Collections, Multithreading, Java, Miscellaneous, Control Flow, OOPS with C++, Stack, C Fundamentals, Arrays & Pointers, Object Oriented Technology, Control Flow & Looping, Introduction to Python
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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