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?

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?

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

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

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

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?

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?

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?

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?

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

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

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

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?

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

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

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

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?

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?

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

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

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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?

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

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

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

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

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

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?

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

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

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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

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 if you have an ordered approach.

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?

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

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?

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

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

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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.

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.

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