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

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.

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

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

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

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

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

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.

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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

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?

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

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

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?

How many centimetres of rope will I need to make another mat just like the one I have here?

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

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

Here are two kinds of spirals for you to explore. What do you notice?

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

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

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.

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?

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

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

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

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

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

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

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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

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

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

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

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

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

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.

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