Stop the Clock game for an adult and child. How can you make sure you always win this game?

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

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.

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

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

Nim-7 game for an adult and child. Who will be the one to take the last counter?

A game for 2 players with similarities to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Got It game for an adult and child. How can you play so that you know you will always win?

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

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

This challenge is about finding the difference between numbers which have the same tens digit.

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Here are two kinds of spirals for you to explore. What do you notice?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

It starts quite simple but great opportunities for number discoveries and patterns!

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?

This challenge asks you to imagine a snake coiling on itself.

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?

Are these statements always true, sometimes true or never true?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Think of a number, square it and subtract your starting number. Is the number youâ€™re left with odd or even? How do the images help to explain this?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

These tasks give learners chance to generalise, which involves identifying an underlying structure.

Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?