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

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 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.

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

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

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

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

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?

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

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.

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

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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.

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

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

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?

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?

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.

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

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?

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

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?

This task follows on from Build it Up and takes the ideas into three dimensions!

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

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

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?

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

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?

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

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!

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

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.

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

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

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

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

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?

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?

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 the empty boxes in the grid with the right shape and colour?

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

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

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

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

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

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?