Being resourceful

  • Arithmagons
    problem

    Arithmagons

    Age
    11 to 16
    Challenge level
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    Can you find the values at the vertices when you know the values on the edges?

  • Stars
    problem

    Stars

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

    Can you work out what step size to take to ensure you visit all the dots on the circle?

  • Square coordinates
    problem

    Square coordinates

    Age
    11 to 14
    Challenge level
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    A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

  • Isosceles Triangles
    problem

    Isosceles triangles

    Age
    11 to 14
    Challenge level
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    Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

  • Consecutive Seven
    problem

    Consecutive seven

    Age
    11 to 14
    Challenge level
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    Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?

  • Ten Hidden Squares
    problem

    Ten hidden squares

    Age
    7 to 14
    Challenge level
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    These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

  • The Thousands Game
    problem

    The thousands game

    Age
    7 to 11
    Challenge level
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    Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?

  • Square It
    problem

    Square it

    Age
    11 to 16
    Challenge level
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    Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

  • Andy's Marbles
    problem

    Andy's marbles

    Age
    7 to 11
    Challenge level
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    Andy had a big bag of marbles but unfortunately the bottom of it split and all the marbles spilled out. Use the information to find out how many there were in the bag originally.

  • On the Edge
    problem

    On the edge

    Age
    11 to 14
    Challenge level
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    If you move the tiles around, can you make squares with different coloured edges?