These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
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 lend themselves to systematic working in the sense that it helps to have an ordered approach.
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
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?
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?
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?
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?
Investigate the different ways you could split up these rooms so that you have double the number.
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?
Can you use this information to work out Charlie's house number?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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.
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.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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. . . .
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 we had 16 light bars which digital numbers could we make? How will you know you've found them all?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
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?
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 will you go about finding all the jigsaw pieces that have one peg and one hole?
In how many ways can you stack these rods, following the rules?
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?
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?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
What could the half time scores have been in these Olympic hockey matches?
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.
What is the best way to shunt these carriages so that each train can continue its journey?