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?

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

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

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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

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?

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?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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.

In this matching game, you have to decide how long different events take.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

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

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.

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?

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

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

This challenge extends the Plants investigation so now four or more children are involved.

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

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

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

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.

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

Investigate the different ways you could split up these rooms so that you have double the number.

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?

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?

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?

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?