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.

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?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

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

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

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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

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.

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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

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?

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?

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 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.

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

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

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?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Roll two red dice and a green dice. Add the two numbers on the red dice and take away the number on the green. What are all the different possibilities that could come up?

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.

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

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

Given the products of adjacent cells, can you complete this Sudoku?

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

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

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.

Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...