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?

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?

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.

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

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 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. . . .

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

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?

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.

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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?

How many different rectangles can you make using this set of rods?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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?

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

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?

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?

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.

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

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?

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

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

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

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

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

A Sudoku that uses transformations as supporting clues.

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?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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?

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

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?

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.

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?