Working systematically

  • Pair Sums
    problem

    Pair sums

    Age
    11 to 14
    Challenge level
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    Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

  • Counting Factors
    problem

    Counting factors

    Age
    11 to 14
    Challenge level
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    Is there an efficient way to work out how many factors a large number has?

  • W Mates
    problem

    W mates

    Age
    16 to 18
    Challenge level
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    Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
  • Magic W
    problem

    Magic W

    Age
    14 to 16
    Challenge level
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    Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

  • Olympic Magic
    problem

    Olympic magic

    Age
    14 to 16
    Challenge level
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    in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

  • Plum Tree
    problem

    Plum tree

    Age
    14 to 18
    Challenge level
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    Label this plum tree graph to make it totally magic!
  • Magic Caterpillars
    problem

    Magic caterpillars

    Age
    14 to 18
    Challenge level
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    Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
  • Instant Insanity
    problem

    Instant insanity

    Age
    11 to 18
    Challenge level
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    Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

  • Latin Numbers
    problem

    Latin numbers

    Age
    14 to 16
    Challenge level
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    Can you create a Latin Square from multiples of a six digit number?

  • Snooker Frames
    problem

    Snooker frames

    Age
    16 to 18
    Challenge level
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    It is believed that weaker snooker players have a better chance of winning matches over eleven frames (i.e. first to win 6 frames) than they do over fifteen frames. Is this true?