Place value

  • Back to the Planet of Vuvv
    problem

    Back to the planet of Vuvv

    Age
    11 to 14
    Challenge level
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    There are two forms of counting on Vuvv - Zios count in base 3 and Zepts count in base 7. Can you work out in which direction the Zios and Zepts were looking, based on the information you're given?

  • Six times five
    problem
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    Six times five

    Age
    11 to 14
    Challenge level
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    How many six digit numbers are there which DO NOT contain a 5?
  • How Many Miles To Go?
    problem
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    How many miles to go?

    Age
    11 to 14
    Challenge level
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    How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?

  • Plastic human skeleton on a blue background.
    problem

    Skeleton

    Age
    11 to 14
    Challenge level
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    Can you reconstruct the long division calculation from the 'skeleton'?

  • Plus Minus
    problem
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    Plus minus

    Age
    14 to 16
    Challenge level
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    Can you explain the surprising results Jo found when she calculated the difference between square numbers?

  • Number rules - OK
    problem
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    Number rules - OK

    Age
    14 to 16
    Challenge level
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    Can you produce convincing arguments that a selection of statements about numbers are true?

  • Latin Numbers
    problem
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    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?

  • 2-Digit Square
    problem
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    2-digit square

    Age
    14 to 16
    Challenge level
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    A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?

  • Place value, integers, ordering and rounding - Short Problems
    problem

    Digit sum

    Age
    14 to 16
    Challenge level
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    What is the sum of all the digits in all the integers from one to one million?

  • Sixty-Seven Squared
    problem
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    Sixty-seven squared

    Age
    16 to 18
    Challenge level
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    Evaluate these powers of 67. What do you notice? Can you convince someone what the answer would be to (a million sixes followed by a 7) squared?