There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

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

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?

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?

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

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, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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

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

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Can you substitute numbers for the letters in these sums?

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?

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

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

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!

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

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

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

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

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

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?

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!

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

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

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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

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

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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

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 out in which order the children are standing in this line?

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.

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

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?

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

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.

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

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?

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.