What two-digit numbers can you make with these two dice? What can't you make?
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Have a go at balancing this equation. Can you find different ways of doing it?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
What happens when you round these three-digit numbers to the nearest 100?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you work out some different ways to balance this equation?
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?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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!
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?
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 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.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?
How many possible necklaces can you find? And how do you know you've found them all?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
How will you go about finding all the jigsaw pieces that have one peg and one hole?
Here are some rods that are different colours. How could I make a yellow rod using white and red rods?
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
What is the best way to shunt these carriages so that each train can continue its journey?
Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?
The Zargoes use almost the same alphabet as English. What does this birthday message say?
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?
My coat has three buttons. How many ways can you find to do up all the buttons?
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?
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!
Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?
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.
The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?
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?
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.
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?
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.