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

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

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

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 see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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

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

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

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.

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

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

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

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

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

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

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

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?

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?

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

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

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

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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.

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.

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

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

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

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

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

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

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.

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

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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?

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

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

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

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 asks you to imagine a snake coiling on itself.

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

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

This challenge encourages you to explore dividing a three-digit number by a single-digit number.

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

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

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