Exploring and noticing

  • Day of the Triffids
    problem

    Day of the Triffids

    Age
    14 to 16
    Challenge level
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    Jasmine buys three different types of plant. How many triffids did she buy?

  • 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?

  • Sheep Talk
    problem

    Sheep talk

    Age
    7 to 11
    Challenge level
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    In sheep talk the only letters used are B and A. A sequence of words is formed by following certain rules. What do you notice when you count the letters in each word?
  • 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 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?

  • Where to Land
    problem

    Where to land

    Age
    14 to 16
    Challenge level
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    Chris is enjoying a swim but needs to get back for lunch. How far along the bank should she land?

  • Sending a Parcel
    problem

    Sending a parcel

    Age
    11 to 14
    Challenge level
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    What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

  • One Million to Seven
    problem

    One million to seven

    Age
    7 to 11
    Challenge level
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    Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?