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

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?

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

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

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.

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

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

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.

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.

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

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, 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.

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

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

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

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

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

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?

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

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.

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

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?

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

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

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

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

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?

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

What happens when you round these three-digit numbers to the nearest 100?

What happens when you round these numbers to the nearest whole number?

This activity involves rounding four-digit numbers to the nearest thousand.

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?

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

This task follows on from Build it Up and takes the ideas into three dimensions!

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Surprise your friends with this magic square trick.

Watch this animation. What do you see? Can you explain why this happens?

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

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.

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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.

This article for primary teachers discusses how we can help learners generalise and prove, using NRICH tasks as examples.

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