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?

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?

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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?

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?

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

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?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

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?

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

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

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?

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?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

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

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

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.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

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

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?

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

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

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

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

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

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

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

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

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.

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

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?

How many models can you find which obey these rules?

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

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

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below 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.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?