In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Find out about Magic Squares in this article written for students. Why are they magic?!
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
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.
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Can you find the chosen number from the grid using the clues?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
Can you find out in which order the children are standing in this line?
Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?
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?
This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.
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!
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.
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!
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?
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?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
My coat has three buttons. How many ways can you find to do up all the buttons?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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?