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?

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?

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?

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?

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?

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

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

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

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

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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

Can you find all the different triangles on these peg boards, and find their angles?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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

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

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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

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

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?

What happens when you try and fit the triomino pieces into these two grids?

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

How long does it take to brush your teeth? Can you find the matching length of time?

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Try this matching game which will help you recognise different ways of saying the same time interval.

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?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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?

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?

This challenge extends the Plants investigation so now four or more children are involved.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?