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

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

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

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.

How many models can you find which obey these rules?

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

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

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

This article for primary teachers suggests ways in which to help children become better at working systematically.

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

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

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

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

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?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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

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?

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?

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

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

How long does it take to brush your teeth? Can you find the matching length of time?

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?

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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

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

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. . . .

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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?

A Sudoku that uses transformations as supporting clues.

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

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

Find all the different shapes that can be made by joining five equilateral triangles edge to edge.