Powers and roots

  • More Magic Potting sheds
    problem

    More magic potting sheds

    Age
    11 to 16
    Challenge level
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    The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?
  • Magic potting sheds
    problem

    Magic potting sheds

    Age
    11 to 16
    Challenge level
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    Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
  • Plus or Minus
    problem

    Plus or minus

    Age
    16 to 18
    Challenge level
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    Make and prove a conjecture about the value of the product of the Fibonacci numbers $F_{n+1}F_{n-1}$.
  • Pythagorean Fibs
    problem

    Pythagorean fibs

    Age
    16 to 18
    Challenge level
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    What have Fibonacci numbers got to do with Pythagorean triples?
  • Fibonacci Fashion
    problem

    Fibonacci fashion

    Age
    16 to 18
    Challenge level
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    What have Fibonacci numbers to do with solutions of the quadratic equation x^2 - x - 1 = 0 ?
  • Golden Eggs
    problem

    Golden eggs

    Age
    16 to 18
    Challenge level
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    Find a connection between the shape of a special ellipse and an infinite string of nested square roots.
  • Lost in Space
    problem

    Lost in space

    Age
    14 to 16
    Challenge level
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    How many ways are there to count 1 - 2 - 3 in the array of triangular numbers? What happens with larger arrays? Can you predict for any size array?
  • Perfectly Square
    problem

    Perfectly square

    Age
    14 to 16
    Challenge level
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    The sums of the squares of three related numbers is also a perfect square - can you explain why?
  • Guesswork
    problem

    Guesswork

    Age
    14 to 16
    Challenge level
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    Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

  • Archimedes and numerical roots
    problem

    Archimedes and numerical roots

    Age
    14 to 16
    Challenge level
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    The problem is how did Archimedes calculate the lengths of the sides of the polygons which needed him to be able to calculate square roots?