Modular arithmetic

  • Odd Stones
    problem
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    Odd Stones

    Age
    14 to 16
    Challenge level
    On a "move" a stone is removed from two of the circles and placed in the third circle. Here are five of the ways that 27 stones could be distributed.
  • Days and Dates
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    Days and Dates

    Age
    11 to 14
    Challenge level

    Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

  • Round and round and round
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    Round and Round and Round

    Age
    11 to 14
    Challenge level

    Where will the point stop after it has turned through 30 000 degrees? I took out my calculator and typed 30 000 ÷ 360. How did this help?

  • Elevenses
    problem
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    Elevenses

    Age
    11 to 14
    Challenge level

    How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?

  • How much can we spend?
    problem
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    How Much Can We Spend?

    Age
    11 to 14
    Challenge level

    A country has decided to have just two different coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?

  • Going round in circles
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    Going Round in Circles

    Age
    11 to 14
    Challenge level

    Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

  • What numbers can we make?
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    What Numbers Can We Make?

    Age
    11 to 14
    Challenge level

    Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

  • Where can we visit?
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    Where Can We Visit?

    Age
    11 to 14
    Challenge level

    Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: ×2 and -5. What do you think?

  • What numbers can we make now?
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    What Numbers Can We Make Now?

    Age
    11 to 14
    Challenge level

    Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

  • Differences
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    Differences

    Age
    11 to 14
    Challenge level

    Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

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