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

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

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

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

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

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

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.

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

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

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?

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?

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.

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

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

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

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

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

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

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

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

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

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

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?

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

Can you find out in which order the children are standing in this line?

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

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?

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?

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

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?

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 brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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?

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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

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?

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

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

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

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?

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?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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?

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?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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