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?
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?
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
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.?
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.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
Can you replace the letters with numbers? Is there only one solution in each case?
Find all the different shapes that can be made by joining five equilateral triangles edge to edge.
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?
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 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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?
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?
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
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?
Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
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?
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?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
Can you use this information to work out Charlie's house number?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
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.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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 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!
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.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
How many rectangles can you find in this shape? Which ones are differently sized and which are 'similar'?
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?
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.