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

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

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

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

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

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

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?

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

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

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

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

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

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.

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?

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?

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?

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

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.

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

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

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.

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

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

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

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

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

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

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

An investigation that gives you the opportunity to make and justify predictions.

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

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

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

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

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

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?

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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.

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?

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?

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.

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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?

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?

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.