Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?
Try out the lottery that is played in a far-away land. What is the chance of winning?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity or play this dice game yourself. How could you make it fair?
How many different rhythms can you make by putting two drums on the wheel?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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 cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these two grids?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?
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....?
Can you hang weights in the right place to make the equaliser balance?
Can you find all the different ways of lining up these Cuisenaire rods?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Use the clues to colour each square.
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?
Investigate the different sounds you can make by putting the owls and donkeys on the wheel.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
Play a dice game of chance
Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?
An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.
Take it in turns to make a triangle on the pegboard. Can you block your opponent?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Exchange the positions of the two sets of counters in the least possible number of moves
A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!
A variant on the game Alquerque
An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .
A game for 2 people that can be played on line or with pens and paper. Combine your knowledege of coordinates with your skills of strategic thinking.
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
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?