Modular arithmetic

There are 51 NRICH Mathematical resources connected to Modular arithmetic
What numbers can we make now?
problem

What numbers can we make now?

Age
11 to 14
Challenge level
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Imagine we have four bags containing numbers from a sequence. What numbers can we make now?

Filling the gaps
problem

Filling the gaps

Age
14 to 16
Challenge level
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Which numbers can we write as a sum of square numbers?
Elevenses
problem

Elevenses

Age
11 to 14
Challenge level
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How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Days and Dates
problem

Days and dates

Age
11 to 14
Challenge level
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Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
How much can we spend?
problem

How much can we spend?

Age
11 to 14
Challenge level
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A country has decided to have just two different coins, 3z and 5z coins. Which totals can be made? Is there a largest total that cannot be made? How do you know?
Going round in circles
problem

Going round in circles

Age
11 to 14
Challenge level
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Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
What numbers can we make?
problem

What numbers can we make?

Age
11 to 14
Challenge level
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Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?

Prime AP
problem

Prime AP

Age
16 to 18
Challenge level
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What can you say about the common difference of an AP where every term is prime?

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?
Where can we visit?
problem

Where can we visit?

Age
11 to 14
Challenge level
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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: x2 and -5. What do you think?