Rectangle Counting Tricks

Duration: 9 min

This video lesson is available to enrolled students.

Return to /learn/RSSB-SENIOR-COMPUTER-INSTRUCTOR/paper-1-logical-reasoning-and-analytical-ability/analytical-reasoning-counting-figures-reasoning/counting-rectangles/asset-rectangle-counting-tricks after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: अनुपात और समानुपात / Ratio and Proportion, Divisibility Rules, मिश्रण और एलिगेशन / Mixture and Alligation, Permutation and Combination, Logarithm, संख्या पद्धति / Number System, महत्तम समापवर्तक और लघुत्तम समापवर्त्य / HCF and LCM, Sequence and Series (Series), समय, चाल और दूरी / Time, Speed and Distance, प्रतिशत / Percentage, औसत / Average, घन क्षेत्रमिति / Solid Mensuration, Age Problems, Arithmetic, Statistics, Probability, लाभ, हानि और बट्टा / Profit, Loss and Discount, साधारण और चक्रवृद्धि ब्याज / Simple and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, सरलीकरण, घातांक और करणी / Simplification, Indices and Surds, समय और कार्य / Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, संख्या पद्धति और संख्या सिद्धांत / Number Systems and Number Theory, निर्देशांक ज्यामिति, सदिश और त्रिविमीय ज्यामिति / Coordinate Geometry, Vectors and 3D Geometry, बहुपद, समीकरण और सम्मिश्र संख्याएँ / Polynomials, Equations and Complex Numbers
  3. Paper-1 & 2 | Data Interpretation: आँकड़ा निर्वचन / Data Interpretation
  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
  5. Paper-1 & 2 | Logical Reasoning and Analytical Ability: श्रेणी / Series, कूट लेखन एवं कूट वाचन / Coding-Decoding, Data Sufficiency, अशाब्दिक तर्क / Non-Verbal Reasoning, Syllogisms, बैठक व्यवस्था एवं पहेलियाँ / Seating Arrangement and Puzzles, रक्त संबंध / Blood Relations, दिशा एवं दूरी / Direction and Distance, Analytical Reasoning (Counting Figures Reasoning), गणितीय संक्रियाएँ एवं लुप्त संख्या / Mathematical Operations and Missing Numbers, कैलेंडर एवं घड़ी / Calendar and Clock, Clock, घन, पासा एवं आकृतियों की गिनती / Cubes, Dice and Figure Counting, वेन आरेख, न्याय वाक्य एवं असमानता / Venn Diagrams, Syllogism and Inequalities, सादृश्यता एवं वर्गीकरण / Analogy and Classification, क्रम एवं रैंकिंग / Order and Ranking, कथन आधारित तार्किक विवेचन / Statement-Based Reasoning, Data Arrangement, वर्णमाला एवं संख्या परीक्षण / Alphabet and Number Test, Crypt Arithmetic
  6. Paper-1 & 2 | Decision Making and Problem Solving: आँकड़ों की पर्याप्तता एवं निर्णय क्षमता / Data Sufficiency and Decision Making
  7. Paper-1 | General Science: वैज्ञानिक उपलब्धियाँ और अनुसंधान / Scientific Achievements and Research, Biology, Chemistry, RSSB Specific Videos
  8. Paper-1 | General Awareness: राज्य विशेष सामान्य ज्ञान / State-Specific General Knowledge, समसामयिकी / Current Affairs
  9. Paper-2 | Fundamentals of Computer: Basics of COA, Number System, Floating Point Rep, Number Representation
  10. Paper - 2 | Digital Logic Systems: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits
  11. Paper-2 | Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Linux OS, Distributed Systems
  12. Paper-2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Relational Calculus, File Organization & Indexing, Transaction Management, Concurrency Control
  13. Paper-2 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  14. Paper-2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  15. Paper 2 | Oops, C++, Java: Language Design, OOPS with C++, Java, .Net Programming, Java Fundamentals
  16. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  17. Paper 2 | Emerging Trends and AI: Emerging Tech Trends, कंप्यूटर के मूल सिद्धांत / Computer Fundamentals, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  18. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Advanced Algorithms
  19. Paper 2 | Data Communication and Network Security: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, 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, Ethical Hacking
  20. Paper-2 I Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  21. Paper-2 | Computer Organization and Architecture: Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations
  22. Paper-2 | Web Development: JavaScript-Basics, HTML Basics, CSS, XML
  23. Pedagogy: वृद्धि और विकास / Growth and Development, Concept of Pedagogy, संज्ञानात्मक प्रक्रियाएँ / Cognitive Processes, विकास के सिद्धांत / Theories of Development, समावेशी शिक्षा / Inclusive Education, Experiential Pedagogy, समाजीकरण और जेंडर / Socialisation and Gender, National Education Policy (NEP) 2020
  24. Live Sessions: RSSB Live Sessions
  25. RSSB Paper 1 - Full Mock Tests:
  26. RSSB Paper 2 - Full Mock Tests:
  27. SCI Previous Year Papers:
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.

Loading lesson…