Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
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?
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?
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?
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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
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?
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....?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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.
Use the clues to colour each square.
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 rhythms can you make by putting two drums on the wheel?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
Can you cover the camel with these pieces?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
What happens when you try and fit the triomino pieces into these two grids?
Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight 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?
Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.
You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?
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?
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?
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.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
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?
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?
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?
Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?
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?
When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.
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?
On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?
Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.
Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.
How many triangles can you make on the 3 by 3 pegboard?
There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?
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.
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.