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

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

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

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

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

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...

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

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?"

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

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?

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.

Can you find all the different ways of lining up these Cuisenaire rods?

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?

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

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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.

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?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

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

A few extra challenges set by some young NRICH members.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

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

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

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

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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?

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

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.

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.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

How many possible necklaces can you find? And how do you know you've found them all?

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

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.

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?

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.