Being curious

  • Tilted Squares
    problem

    Tilted squares

    Age
    11 to 14
    Challenge level
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    It's easy to work out the areas of most squares that we meet, but what if they were tilted?

  • Your number is...
    problem

    Your number is...

    Age
    7 to 14
    Challenge level
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    Think of a number and follow the machine's instructions... I know what your number is! Can you explain how I know?
  • More Number Pyramids
    problem

    More number pyramids

    Age
    11 to 14
    Challenge level
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    When number pyramids have a sequence on the bottom layer, some interesting patterns emerge...

  • Pair Products
    problem

    Pair products

    Age
    14 to 16
    Challenge level
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    Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

  • Special Numbers
    problem

    Special numbers

    Age
    11 to 14
    Challenge level
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    My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

  • Triangles and petals
    problem

    Triangles and petals

    Age
    14 to 16
    Challenge level
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    An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

  • The Brown Family
    problem

    The Brown family

    Age
    5 to 7
    Challenge level
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    Use the information about Sally and her brother to find out how many children there are in the Brown family.

  • 5 on the clock
    problem

    5 on the clock

    Age
    7 to 11
    Challenge level
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    On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

  • Three by One
    problem

    Three by one

    Age
    16 to 18
    Challenge level
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    There are many different methods to solve this geometrical problem - how many can you find?
  • Hexy-Metry
    problem

    Hexy-metry

    Age
    14 to 16
    Challenge level
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    A hexagon, with sides alternately a and b units in length, is inscribed in a circle. How big is the radius of the circle?