Being resourceful

  • Filling the gaps
    problem
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    Filling the Gaps

    Age
    14 to 16
    Challenge level
    2 out of 3

    Which numbers can we write as a sum of square numbers?

  • Attractive Tablecloths
    problem
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    Attractive Tablecloths

    Age
    14 to 16
    Challenge level
    2 out of 3

    Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

  • Odds and Evens made fair
    problem
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    Odds and Evens Made Fair

    Age
    14 to 16
    Challenge level
    2 out of 3

    In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.

  • Difference of Two Squares
    problem
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    Difference of Two Squares

    Age
    14 to 16
    Challenge level
    2 out of 3

    What is special about the difference between squares of numbers adjacent to multiples of three?

  • Pythagoras Perimeters
    problem
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    Pythagoras Perimeters

    Age
    14 to 16
    Challenge level
    2 out of 3

    If you know the perimeter of a right angled triangle, what can you say about the area?

  • Multiplication arithmagons
    problem
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    Multiplication Arithmagons

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you find the values at the vertices when you know the values on the edges of these multiplication arithmagons?

  • Puzzling Place Value
    problem
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    Puzzling Place Value

    Age
    14 to 16
    Challenge level
    2 out of 3

    Can you explain what is going on in these puzzling number tricks?

  • Bendy Quad
    problem
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    Bendy Quad

    Age
    14 to 16
    Challenge level
    3 out of 3

    Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.

  • Latin Numbers
    problem
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    Latin Numbers

    Age
    14 to 16
    Challenge level
    3 out of 3

    Can you create a Latin Square from multiples of a six digit number?

  • Two blank square picture frames on a wooden floor.
    problem
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    2-Digit Square

    Age
    14 to 16
    Challenge level
    3 out of 3

    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?