Being curious

  • What's it worth?
    problem

    What's it worth?

    Age
    11 to 16
    Challenge level
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    There are lots of different methods to find out what the shapes are worth - how many can you find?

  • Twenty Divided into Six
    problem

    Twenty divided into six

    Age
    7 to 11
    Challenge level
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    Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

  • Amy's Dominoes
    problem

    Amy's dominoes

    Age
    7 to 11
    Challenge level
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    Amy has a box containing domino pieces but she does not think it is a complete set. Which of her domino pieces are missing?

  • problem

    Abundant numbers

    Age
    7 to 11
    Challenge level
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    48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

  • problem

    How many times?

    Age
    7 to 11
    Challenge level
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    On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

  • Marbles in a box
    problem

    Marbles in a box

    Age
    11 to 16
    Challenge level
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    How many winning lines can you make in a three-dimensional version of noughts and crosses?

  • Arclets
    problem

    Arclets

    Age
    14 to 16
    Challenge level
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    Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".
  • Blue and White
    problem

    Blue and white

    Age
    11 to 14
    Challenge level
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    Identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

  • Which Scripts?
    problem

    Which scripts?

    Age
    7 to 11
    Challenge level
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    There are six numbers written in five different scripts. Can you sort out which is which?

  • What's Possible?
    problem

    What's possible?

    Age
    14 to 16
    Challenge level
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    Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?