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.

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

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

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

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.

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

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

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

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

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 ...?

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?

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

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?

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.

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

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?

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

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

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?

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

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

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

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.

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?

How many trapeziums, of various sizes, are hidden in this picture?

In how many ways can you stack these rods, following the rules?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

Can you use this information to work out Charlie's house number?

What is the best way to shunt these carriages so that each train can continue its journey?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

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 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?

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, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

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

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

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

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

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