Can you fill in the empty boxes in the grid with the right shape and colour?

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?

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

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

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

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?

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.

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?

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?

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

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

Find all the numbers that can be made by adding the dots on two dice.

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?

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!

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?

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?

Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.

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?

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!

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?

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?

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.

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.

Use these head, body and leg pieces to make Robot Monsters which are different heights.

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

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?

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

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

Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?

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?

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?

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?

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.

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?

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

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