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

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

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

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 explain the strategy for winning this game with any target?

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

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

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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

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

A game for 2 players. Set out 16 counters in rows of 1,3,5 and 7. Players take turns to remove any number of counters from a row. The player left with the last counter looses.

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.

Try entering different sets of numbers in the number pyramids. How does the total at the top change?

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

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

The Egyptians expressed all fractions as the sum of different unit fractions. Here is a chance to explore how they could have written different fractions.

Can all unit fractions be written as the sum of two unit fractions?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

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

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

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

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

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.

We can show that (x + 1)² = x² + 2x + 1 by considering the area of an (x + 1) by (x + 1) square. Show in a similar way that (x + 2)² = x² + 4x + 4

Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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 the values at the vertices when you know the values on the edges?

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

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?

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

Delight your friends with this cunning trick! Can you explain how it works?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

Pick the number of times a week that you eat chocolate. This number must be more than one but less than ten. Multiply this number by 2. Add 5 (for Sunday). Multiply by 50... Can you explain why it. . . .

You can work out the number someone else is thinking of as follows. Ask a friend to think of any natural number less than 100. Then ask them to tell you the remainders when this number is divided by. . . .

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

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

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

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

If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.

How could Penny, Tom and Matthew work out how many chocolates there are in different sized boxes?

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

Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.

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

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

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