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?

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

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

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

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?

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?

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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

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. . . .

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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

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?

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

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?

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

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

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 interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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?

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

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

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?

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

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

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

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

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?

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

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

My coat has three buttons. How many ways can you find to do up all the buttons?

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?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

What happens when you try and fit the triomino pieces into these two grids?

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

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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.

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

Penta people, the Pentominoes, always build their houses from five square rooms. I wonder how many different Penta homes you can create?

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?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?