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.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
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?
Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
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.
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?
Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
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?
These activities lend themselves to systematic working in the sense that it helps if you 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 ...?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
In how many ways can you stack these rods, following the rules?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
This article for primary teachers suggests ways in which to help children become better at working systematically.
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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.
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?
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.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
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?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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.
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
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?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
I like to walk along the cracks of the paving stones, but not the outside edge of the path itself. How many different routes can you find for me to take?