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.

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.

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?

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.

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.

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?

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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

Try this matching game which will help you recognise different ways of saying the same time interval.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

A challenging activity focusing on finding all possible ways of stacking rods.

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

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?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

Try out the lottery that is played in a far-away land. What is the chance of winning?

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Can you find all the different triangles on these peg boards, and find their angles?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

My coat has three buttons. How many ways can you find to do up all the buttons?

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

What could the half time scores have been in these Olympic hockey matches?

This challenge extends the Plants investigation so now four or more children are involved.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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.

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?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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.

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Can you use the information to find out which cards I have used?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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.

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?