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?

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

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

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

Can you find out in which order the children are standing in this line?

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?

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?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks.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

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

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 working in a systematic way will ensure none are left out.

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

This problem is based on the story of the Pied Piper of Hamelin. 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 focuses on finding the sum and difference of pairs of two-digit numbers.

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?

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?

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

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

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 could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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!

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.

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

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

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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?

Can you substitute numbers for the letters in these sums?

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?

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.

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!

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

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

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

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?

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

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

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

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

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?

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

Number problems at primary level that require careful consideration.

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?

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.