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?

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

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

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?

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

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

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

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?

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

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.

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Can you explain the strategy for winning this game with any target?

It would be nice to have a strategy for disentangling any tangled ropes...

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

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.

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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.

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.

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

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

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

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

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

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.

Try out this number trick. What happens with different starting numbers? What do you notice?

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?

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

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

Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Find the sum of all three-digit numbers each of whose digits is odd.

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.

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. . . .

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?

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

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

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

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

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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.

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?”

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?