Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possible answers?

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?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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?

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

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

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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. . . .

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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?

A few extra challenges set by some young NRICH members.

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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?

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.

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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.

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

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.

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What is the best way to shunt these carriages so that each train can continue its journey?

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

A Sudoku that uses transformations as supporting clues.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

Find out about the lottery that is played in a far-away land. What is the chance of winning?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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

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

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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

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?

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

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?