Square Counting Tricks

Duration: 25 min

This video lesson is available to enrolled students.

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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 comprehensive tutorial on counting squares in a grid, presented as a lecture. The instructor begins by introducing the topic with a title slide and then demonstrates a method for counting squares in a 4x4 grid by systematically summing the squares of different sizes: 4x4, 3x3, 2x2, and 1x1. He explains that the total number of squares is the sum of the squares of the first n natural numbers, where n is the number of rows or columns. The formula 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 is derived and applied to a 4x4 grid, yielding a total of 30 squares. The lecture then transitions to a more complex problem involving a 50x50 grid, where the same formula is used to calculate the total number of squares. The instructor also demonstrates a different type of grid, a 4x4 grid with overlapping squares, and applies the same counting method. The video concludes with a final summary of the key concepts and a 'Thanks for Watching' screen.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video opens with a title slide that reads "SQUARE COUNTING TRICKS". The instructor, a man in a grey polo shirt, stands in front of a whiteboard and begins his lecture. He introduces the topic of counting squares in a grid, explaining that the number of squares can be found by summing the squares of the first n natural numbers, where n is the number of rows or columns. He mentions that this is a common question in competitive exams like the CAT and other national qualifier tests.

  2. 2:00 – 5:00 02:00-05:00

    The instructor draws a 4x4 grid on the whiteboard. He explains the method for counting squares by considering different sizes. He writes the numbers 1, 2, 3, 4 along the top and left side of the grid to represent the row and column indices. He then begins to count the squares of each size: 4x4, 3x3, 2x2, and 1x1. He explains that there is 1 square of size 4x4, 4 squares of size 3x3, 9 squares of size 2x2, and 16 squares of size 1x1. He writes the calculation 1 + 4 + 9 + 16 = 30 on the board.

  3. 5:00 – 10:00 05:00-10:00

    The instructor explains the formula for the sum of squares of the first n natural numbers: 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6. He writes this formula on the whiteboard and explains that it can be used to quickly calculate the total number of squares in an n x n grid. He applies the formula to the 4x4 grid, substituting n=4, and calculates 4(4+1)(2*4+1)/6 = 4*5*9/6 = 30. He then moves on to a more complex problem involving a 50x50 grid, where he applies the same formula to calculate the total number of squares.

  4. 10:00 – 15:00 10:00-15:00

    The instructor draws a different type of grid on the whiteboard, a 4x4 grid with overlapping squares. He explains that the same method can be used to count the squares in this grid. He counts the squares of each size: 4x4, 3x3, 2x2, and 1x1. He writes the calculation 1 + 4 + 9 + 16 = 30 on the board. He then explains that the total number of squares in a 4x4 grid is 30, regardless of the arrangement of the squares.

  5. 15:00 – 20:00 15:00-20:00

    The instructor draws a 4x4 grid on the whiteboard and explains that the total number of squares in a 4x4 grid is 30. He then draws a 50x50 grid and applies the formula 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 to calculate the total number of squares. He substitutes n=50 into the formula and calculates 50(50+1)(2*50+1)/6 = 50*51*101/6 = 42925. He explains that the total number of squares in a 50x50 grid is 42925.

  6. 20:00 – 25:00 20:00-25:00

    The instructor draws a 4x4 grid on the whiteboard and explains that the total number of squares in a 4x4 grid is 30. He then draws a 50x50 grid and applies the formula 1² + 2² + 3² + ... + n² = n(n+1)(2n+1)/6 to calculate the total number of squares. He substitutes n=50 into the formula and calculates 50(50+1)(2*50+1)/6 = 50*51*101/6 = 42925. He explains that the total number of squares in a 50x50 grid is 42925.

  7. 25:00 – 25:28 25:00-25:28

    The video ends with a 'Thanks for Watching' screen. The screen has a blue background with a network of lines and dots. The text 'THANKS FOR WATCHING' is displayed in white capital letters in the center of the screen.

The video provides a clear and structured lesson on counting squares in a grid. It begins with a simple 4x4 grid, demonstrating the method of counting squares of different sizes and then introduces the mathematical formula for the sum of squares. The instructor then applies this formula to a larger 50x50 grid, showing how the method scales. The video also covers a more complex grid with overlapping squares, reinforcing the concept. The progression from a simple example to a more complex one, and the clear explanation of the formula, make the lesson effective for students preparing for competitive exams.

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