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

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.

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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?

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

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

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

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?

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?

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.

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

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

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

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?

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

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

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

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

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.

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.

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?

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

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

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?

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?

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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.

Can you find the chosen number from the grid using the clues?

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....?

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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

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?

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?

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.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

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

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

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!

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?

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?

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?