Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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

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.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

A Sudoku with clues given as sums of entries.

How many different triangles can you make on a circular pegboard that has nine pegs?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

What is the best way to shunt these carriages so that each train can continue its journey?

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

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

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

How many trains can you make which are the same length as Matt's, using rods that are identical?

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.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What happens when you try and fit the triomino pieces into these two grids?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

Design an arrangement of display boards in the school hall which fits the requirements of different people.

How many different rhythms can you make by putting two drums on the wheel?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.