The clues for this Sudoku are the product of the numbers in adjacent squares.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A few extra challenges set by some young NRICH members.

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

These eleven shapes each stand for a different number. Can you use the number sentences to work out what they are?

You need to find the values of the stars before you can apply normal Sudoku rules.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Given the products of adjacent cells, can you complete this Sudoku?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

Investigate the different ways you could split up these rooms so that you have double the number.

How many different symmetrical shapes can you make by shading triangles or squares?

Can you work out some different ways to balance this equation?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

The pages of my calendar have got mixed up. Can you sort them out?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

In this matching game, you have to decide how long different events take.

There are lots of different methods to find out what the shapes are worth - how many can you find?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?