Square Counting Tricks

Duration: 25 min

This video lesson is available to enrolled students.

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Module outline

  1. About the Course: About the Course
  2. Paper-1 & 2 | Basic Numeracy: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Logarithm, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Percentage, Average, Mensuration and Geometry, Age Problems, Arithmetic, Statistics, Probability, Profit and Loss, Simple Interest and Compound Interest, Partnership, Speed Mathematics and Basic Mathematics, Algebra, Powers and Exponents (Surds and Indices), Time and Work, Pipe and Cistern, RSSB Specific Videos - Basic Numeracy
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  4. Paper-1 & 2 | General Mental Ability: Mental Ability, RSSB Specific Videos - Mental Ability
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  24. Paper 1 - Full Mock Tests:
  25. Paper 2 - Full Mock Tests:
  26. BCI 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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