How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
The pages of my calendar have got mixed up. Can you sort them out?
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.
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?
During the third hour after midnight the hands on a clock point in the same direction (so one hand is over the top of the other). At what time, to the nearest second, does this happen?
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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?
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.?
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?
In this matching game, you have to decide how long different events take.
Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.
Use the clues about the symmetrical properties of these letters to place them on the grid.
Ben has five coins in his pocket. How much money might he have?
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?
A challenging activity focusing on finding all possible ways of stacking rods.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
In how many ways can you stack these rods, following the rules?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
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?
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 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?
In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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 ...?
Can you draw a square in which the perimeter is numerically equal to the area?
Investigate the different ways you could split up these rooms so that you have double the number.
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?
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!
What could the half time scores have been in these Olympic hockey matches?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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.
Can you make square numbers by adding two prime numbers together?
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?
Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?
El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?
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?
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?