Conjecturing and generalising

  • Crossings
    problem

    Crossings

    Age
    7 to 11
    Challenge level
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    In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
  • Number Differences
    problem

    Number differences

    Age
    7 to 11
    Challenge level
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    Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

  • More Numbers in the Ring
    problem

    More numbers in the ring

    Age
    5 to 7
    Challenge level
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    If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

  • Ring a Ring of Numbers
    problem

    Ring a ring of numbers

    Age
    5 to 7
    Challenge level
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    Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

  • Carrying Cards
    problem

    Carrying cards

    Age
    7 to 11
    Challenge level
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    These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

  • Cyclic Triangles
    problem

    Cyclic triangles

    Age
    16 to 18
    Challenge level
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    Make and prove a conjecture about the cyclic quadrilateral inscribed in a circle of radius r that has the maximum perimeter and the maximum area.
  • 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
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    Can you work out what step size to take to ensure you visit all the dots on the circle?

  • 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.

  • Hundred Square Poster
    problem

    Hundred square

    Age
    5 to 11
    Challenge level
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    A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?