Can you work out how to balance this equaliser? You can put more than one weight on a hook.
What is the best way to shunt these carriages so that each train can continue its journey?
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?
10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?
A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?
Can you cover the camel with these pieces?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?
You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?
How many different rhythms can you make by putting two drums on the wheel?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these two grids?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Use the clues to colour each square.
An activity making various patterns with 2 x 1 rectangular tiles.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
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.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.
How many different triangles can you make on a circular pegboard that has nine pegs?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?
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.
This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
In this matching game, you have to decide how long different events take.
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.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?
Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?
These practical challenges are all about making a 'tray' and covering it with paper.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .