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?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
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?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
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.
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
Tim had nine cards each with a different number from 1 to 9 on it. How could he have put them into three piles so that the total in each pile was 15?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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.
There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
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?
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
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!
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
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?
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?
In how many ways can you stack these rods, following the rules?
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?