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?

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?

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?

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?

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

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 out in which order the children are standing in this line?

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

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

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

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.

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

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

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

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 if you have an ordered approach.

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 to 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?

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.

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

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

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?

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?

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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

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

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

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

How many different shapes can you make by putting four right- angled isosceles triangles together?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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

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 information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

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?

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?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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