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

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 find all the different ways of lining up these Cuisenaire rods?

Can you find out in which order the children are standing in this line?

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?

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

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

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.

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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?

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?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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?

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

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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

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

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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.

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

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

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?

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?

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

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?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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?

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 do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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.

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

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