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.

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?

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

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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.

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?

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.

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

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?

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

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?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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.

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?

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

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

In this matching game, you have to decide how long different events take.

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

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

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

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

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

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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

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

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

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

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.

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

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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