Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
This article for primary teachers suggests ways in which to help children become better at working systematically.
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?
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!
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
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 Zargoes use almost the same alphabet as English. What does this birthday message say?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
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 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.
Can you use this information to work out Charlie's house number?
Investigate the different ways you could split up these rooms so that you have double the number.
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
How will you go about finding all the jigsaw pieces that have one peg and one hole?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
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?
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.
My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?
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?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
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?
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.
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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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 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?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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.
In how many ways can you stack these rods, following the rules?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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.?