Modular arithmetic

There are 51 NRICH Mathematical resources connected to Modular arithmetic

problem

Favourite

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?

problem

Favourite

Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?

problem

Favourite

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?

problem

Favourite

Prime ap

Age

16 to 18

Challenge level

What can you say about the common difference of an AP where every term is prime?

problem

Favourite

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?

problem

Favourite

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: x2 and -5. What do you think?

problem

Favourite

Guesswork

Age

14 to 16

Challenge level

Ask a friend to choose a number between 1 and 63. By identifying which of the six cards contains the number they are thinking of it is easy to tell them what the number is.

problem

Favourite

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.

problem

Favourite

Take three from five

Age

11 to 16

Challenge level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

problem

Favourite

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?

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For younger learners

Modular arithmetic

What numbers can we make now?

Filling the gaps

What numbers can we make?

Prime ap

Differences

Where can we visit?

Guesswork

Odd stones

Take three from five

Round and round and round