Modular arithmetic

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

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?

Happy \birthDay
problem

Happy birthDay

Age
16 to 18
Challenge level
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Can you interpret this algorithm to determine the day on which you were born?
Filling the gaps
problem
Favourite

Filling the gaps

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

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?

Sixinit
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Sixinit

Age
16 to 18
Challenge level
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Choose any whole number n, cube it, add 11n, and divide by 6. What do you notice?
Going round in circles
problem
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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?
How much can we spend?
problem
Favourite

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?
Elevenses
problem
Favourite

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?
Zeller's Birthday
problem

Zeller's Birthday

Age
14 to 16
Challenge level
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What day of the week were you born on? Do you know? Here's a way to find out.
Round and round and round
problem
Favourite

Round and round and round

Age
11 to 14
Challenge level
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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?