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

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

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. . . .

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

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?

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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?

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?

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

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

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

This challenge is about finding the difference between numbers which have the same tens digit.

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

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.

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

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

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?

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'.

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?

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.

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

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

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

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

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

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?

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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?

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

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.

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.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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

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

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

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?

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?

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?

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.

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

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

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

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.