Exploring and noticing

  • Differences
    problem

    Differences

    Age
    11 to 14
    Challenge level
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    Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

  • Trapezium made of wooden tangram pieces, including a square and a parallelogram.
    problem

    Quad in quad

    Age
    14 to 18
    Challenge level
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    Join the midpoints of a quadrilateral to get a new quadrilateral. What is special about it?

  • Tet-Trouble
    problem

    Tet-trouble

    Age
    14 to 16
    Challenge level
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    Is it possible to have a tetrahedron whose six edges have lengths 10, 20, 30, 40, 50 and 60 units?

  • Dozens
    problem

    Dozens

    Age
    7 to 14
    Challenge level
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    Can you select the missing digit(s) to find the largest multiple?

  • A Mean Tetrahedron
    problem

    A mean tetrahedron

    Age
    11 to 14
    Challenge level
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    Can you number the vertices, edges and faces of a tetrahedron so that the number on each edge is the mean of the numbers on the adjacent vertices and the mean of the numbers on the adjacent faces?
  • Hallway Borders
    problem

    Hallway borders

    Age
    11 to 14
    Challenge level
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    What are the possible dimensions of a rectangular hallway if the number of tiles around the perimeter is exactly half the total number of tiles?
  • problem

    Number sandwiches

    Age
    7 to 14
    Challenge level
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    Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

  • Two Ladders
    problem

    Two ladders

    Age
    14 to 16
    Challenge level
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    Two ladders are propped up against facing walls. At what height do the ladders cross?

  • Triangle midpoints
    problem

    Triangle midpoints

    Age
    14 to 16
    Challenge level
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    You are only given the three midpoints of the sides of a triangle. How can you construct the original triangle?

  • 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?