A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?
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.
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 ...?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?
An investigation that gives you the opportunity to make and justify predictions.
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?
Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
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?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?
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?
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.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.