Difference of two squares

  • Hollow Squares
    problem

    Hollow squares

    Age
    14 to 16
    Challenge level
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    Which armies can be arranged in hollow square fighting formations?
  • Difference of Two Squares
    problem

    Difference of two squares

    Age
    14 to 16
    Challenge level
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    What is special about the difference between squares of numbers adjacent to multiples of three?
  • Particularly general
    problem

    Particularly general

    Age
    16 to 18
    Challenge level
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    By proving these particular identities, prove the existence of general cases.
  • Square Product
    problem

    Square product

    Age
    14 to 16
    Challenge level
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    Weekly Problem 10 - 2011
    Will this product give a perfect square?
  • Why 24?
    problem

    Why 24?

    Age
    14 to 16
    Challenge level
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    Take any prime number greater than 3 , square it and subtract one. Working on the building blocks will help you to explain what is special about your results.
  • What's Possible?
    problem

    What's possible?

    Age
    14 to 16
    Challenge level
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    Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

  • Plus Minus
    problem

    Plus minus

    Age
    14 to 16
    Challenge level
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    Can you explain the surprising results Jo found when she calculated the difference between square numbers?
  • Odd Differences
    problem

    Odd differences

    Age
    14 to 16
    Challenge level
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    The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.
  • 2-Digit Square
    problem

    2-digit square

    Age
    14 to 16
    Challenge level
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    A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
  • DOTS Division
    problem

    DOTS division

    Age
    14 to 16
    Challenge level
    filled star filled star filled star

    Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.