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

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?

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.

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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?

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?

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

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

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

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

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?

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?

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

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....?

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.

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.

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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?

How many possible necklaces can you find? And how do you know you've found them all?

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

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?

This dice train has been made using specific rules. How many different trains can you make?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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

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

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Investigate the different ways you could split up these rooms so that you have double the number.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

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?

Can you find all the ways to get 15 at the top of this triangle of numbers?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

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!

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?