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

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?

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?

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.

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

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

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?

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

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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.

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

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?

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?

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.

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. . . .

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

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

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

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

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

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.

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

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

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

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

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?

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

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

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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!

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