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

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?"

Given the products of diagonally opposite cells - can you complete this Sudoku?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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...

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

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 few extra challenges set by some young NRICH members.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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.

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Two sudokus in one. Challenge yourself to make the necessary connections.

Two sudokus in one. Challenge yourself to make the necessary connections.

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

A Sudoku that uses transformations as supporting clues.

This Sudoku requires you to do some working backwards before working forwards.

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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 put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

The items in the shopping basket add and multiply to give the same amount. What could their prices be?