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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Arrange 3 red, 3 blue and 3 yellow counters into a three-by-three square grid, so that there is only one of each colour in every row and every column
Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?
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.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Can you use this information to work out Charlie's house number?
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?
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?
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.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?
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?
If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
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!
My cousin was 24 years old on Friday April 5th in 1974. On what day of the week was she born?
How many possible necklaces can you find? And how do you know you've found them all?
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?
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
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?
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 create jigsaw pieces which are based on a square shape, with at least one peg and one hole?
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
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?
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 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.
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
The Zargoes use almost the same alphabet as English. What does this birthday message say?
How many trapeziums, of various sizes, are hidden in this picture?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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.
In how many ways can you stack these rods, following the rules?