Working systematically

  • Quadratic Matching
    problem

    Quadratic Matching

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

    Can you match each graph to one of the statements?

  • Olympic Magic
    problem

    Olympic Magic

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

    in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

  • Magic W
    problem

    Magic W

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

    Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

  • Tetrahedra Tester
    problem

    Tetrahedra Tester

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

    An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

  • Twin Line-Swapping Sudoku
    problem

    Twin Line-Swapping Sudoku

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

    A pair of Sudoku puzzles that together lead to a complete solution.

  • The Fastest Cyclist
    problem

    The Fastest Cyclist

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

    Andy is desperate to reach John o'Groats first. Can you devise a winning race plan?

  • Gridlines
    problem

    Gridlines

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

    How many triples of points are there in this 4×4 array that lie on a straight line?

  • Symmetricality
    problem

    Symmetricality

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

    Five equations and five unknowns. Is there an easy way to find the unknown values?

  • Flipping Twisty Matrices
    problem

    Flipping Twisty Matrices

    Age
    14 to 18
    Challenge level
    filled star empty star empty star

    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
    filled star empty star empty star

    A Sudoku based on clues that give the differences between adjacent cells.