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

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

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

How many possible necklaces can you find? And how do you know you've found them all?

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

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

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

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

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

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

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?

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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.

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.

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

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

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

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?

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?

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

What could the half time scores have been in these Olympic hockey matches?

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?

How many different rectangles can you make using this set of rods?

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.

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

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

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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?

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

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?

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

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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

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.

The pages of my calendar have got mixed up. Can you sort them out?

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.