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?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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.
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Ben has five coins in his pocket. How much money might he have?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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!
In how many ways can you stack these rods, following the rules?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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?
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.?
How many trapeziums, of various sizes, are hidden in this picture?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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.
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?
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.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
What could the half time scores have been in these Olympic hockey matches?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
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.
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?
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
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.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
Using all ten cards from 0 to 9, rearrange them to make five prime numbers. Can you find any other ways of doing it?
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 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.
My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?
There are lots of different methods to find out what the shapes are worth - how many can you find?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
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 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 ...?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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?