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?

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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?

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 1-3 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?

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.

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

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.

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

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?

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

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?

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?

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

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?

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

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?

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!

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 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?

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.

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?

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.

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.

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?

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

Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?

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

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

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

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

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?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is 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!

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?

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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

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?

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?

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?

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