Conjecturing and generalising

  • A green frog.
    problem

    Frogs

    Age
    11 to 14
    Challenge level
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    How many moves does it take to swap over some red and blue frogs? Do you have a method?

  • Nim-7
    problem

    Nim-7

    Age
    5 to 11
    Challenge level
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    Can you work out how to win this game of Nim? Does it matter if you go first or second?
  • Egyptian Fractions
    problem

    Egyptian fractions

    Age
    11 to 14
    Challenge level
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    The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

  • Cubes within Cubes
    problem

    Cubes within cubes

    Age
    7 to 14
    Challenge level
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    We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

  • problem

    Two primes make one square

    Age
    7 to 11
    Challenge level
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    Can you make square numbers by adding two prime numbers together?

  • Square Corners
    problem

    Square corners

    Age
    7 to 11
    Challenge level
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    What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

  • problem

    Reach 100

    Age
    7 to 11
    Challenge level
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    Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

  • Path to the Stars
    problem

    Path to the stars

    Age
    7 to 11
    Challenge level
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    Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?
  • 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?

  • Calendar Calculations
    problem

    Calendar calculations

    Age
    7 to 11
    Challenge level
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    Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?