Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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.?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
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.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
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?
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?
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!
On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
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.
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?
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.
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!
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?
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
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?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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?
Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
These activities lend themselves to systematic working in the sense that it helps to 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!
In how many ways can you stack these rods, following the rules?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?