Working systematically

  • LCM Sudoku
    problem
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    LCM Sudoku

    Age
    14 to 16
    Challenge level
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    Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

  • Difference Sudoku
    problem
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    Difference Sudoku

    Age
    14 to 16
    Challenge level
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    Use the differences to find the solution to this Sudoku.

  • Symmetricality
    problem

    Symmetricality

    Age
    14 to 18
    Challenge level
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    Five equations and five unknowns. Is there an easy way to find the unknown values?

  • Parabolic Patterns
    problem
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    Parabolic Patterns

    Age
    14 to 18
    Challenge level
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    The illustration shows the graphs of fifteen functions. Two of them have equations $y=x^2$ and $y=-(x-4)^2$. Find the equations of all the other graphs.

  • Flipping Twisty Matrices
    problem

    Flipping Twisty Matrices

    Age
    14 to 18
    Challenge level
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    Investigate the transformations of the plane given by the 2 by 2 matrices with entries taking all combinations of values 0, -1 and +1.

  • Pole Star Sudoku
    problem

    Pole Star Sudoku

    Age
    14 to 18
    Challenge level
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    A Sudoku based on clues that give the differences between adjacent cells.

  • Twin chute-swapping Sudoku
    problem

    Twin Chute-Swapping Sudoku

    Age
    14 to 18
    Challenge level
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    A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

  • Vector walk
    problem
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    Vector Walk

    Age
    14 to 18
    Challenge level
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    Starting with two basic vector steps, which destinations can you reach on a vector walk?

  • Difference Dynamics
    problem

    Difference Dynamics

    Age
    14 to 18
    Challenge level
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    Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?
  • Stadium Sightline
    problem

    Stadium Sightline

    Age
    14 to 18
    Challenge level
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    How would you design the tiering of seats in a stadium so that all spectators have a good view?