Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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.
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?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
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?
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?
Use the clues to colour each square.
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?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?
What is the best way to shunt these carriages so that each train can continue its journey?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
Make your own double-sided magic square. But can you complete both sides once you've made the pieces?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
In this matching game, you have to decide how long different events take.
Investigate the different ways you could split up these rooms so that you have double the number.
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?
Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.
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....?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.
How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?
A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
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?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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. . . .
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?