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?
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?
Make one big triangle so the numbers that touch on the small triangles add to 10.
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
What happens when you try and fit the triomino pieces into these two grids?
Can you cover the camel with these pieces?
This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?
Can you find all the different ways of lining up these Cuisenaire rods?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Use the clues to colour each square.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Sort the houses in my street into different groups. Can you do it in any other ways?
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?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
How many different triangles can you make on a circular pegboard that has nine pegs?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you find all the different triangles on these peg boards, and find their angles?
Find out what a "fault-free" rectangle is and try to make some of your own.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
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?
Take it in turns to place a domino on the grid. One to be placed horizontally and the other vertically. Can you make it impossible for your opponent to play?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
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....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Move just three of the circles so that the triangle faces in the opposite direction.
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
If you have only four weights, where could you place them in order to balance this equaliser?
If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five 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 sort these triangles into three different families and explain how you did it?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
Try out the lottery that is played in a far-away land. What is the chance of winning?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?