Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Find out what a "fault-free" rectangle is and try to make some of your own.
Can you find all the different ways of lining up these Cuisenaire rods?
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 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?
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?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
Can you find all the different triangles on these peg boards, and find their angles?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
These rectangles have been torn. How many squares did each one have inside it before it was ripped?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Try out the lottery that is played in a far-away land. What is the chance of winning?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?
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?
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?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
An activity making various patterns with 2 x 1 rectangular tiles.
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
Tim's class collected data about all their pets. Can you put the animal names under each column in the block graph using the information?
How many triangles can you make on the 3 by 3 pegboard?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?
What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?
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?
Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.
If we had 16 light bars which digital numbers could we make? How will you know you've found them all?
Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?
Investigate the different ways you could split up these rooms so that you have double the number.
You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Stuart's watch loses two minutes every hour. Adam's watch gains one minute every hour. Use the information to work out what time (the real time) they arrived at the airport.
How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?
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?
Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.