Conjecturing and generalising

  • 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?

  • Reach 100
    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?
  • 1 Step 2 Step
    problem

    1 step 2 step

    Age
    11 to 14
    Challenge level
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    Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
  • problem

    Flashing lights

    Age
    7 to 11
    Challenge level
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    Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

  • 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?

  • Zios and Zepts
    problem

    Zios and Zepts

    Age
    7 to 11
    Challenge level
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    On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

  • Rope Mat
    problem

    Rope mat

    Age
    7 to 11
    Challenge level
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    How many centimetres of rope will I need to make another mat just like the one I have here?