Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.
This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.
Find all the numbers that can be made by adding the dots on two dice.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
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?
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.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
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?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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.
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Investigate the different ways you could split up these rooms so that you have double the number.
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
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?
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?
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?
In how many ways can you stack these rods, following the rules?
This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.
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.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
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?
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. . . .
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.
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?
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'.
This dice train has been made using specific rules. How many different trains can you make?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?