Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
If you have only four weights, where could you place them in order to balance this equaliser?
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.
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!
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
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?
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?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Can you hang weights in the right place to make the equaliser balance?
Here is a chance to play a version of the classic Countdown Game.
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.
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?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?
Can you work out how to balance this equaliser? You can put more than one weight on a hook.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Use the number weights to find different ways of balancing the equaliser.
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
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 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?
Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.
Choose a symbol to put into the number sentence.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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?
Match the halves.
Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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 complete this jigsaw of the multiplication square?
Use the interactivity to find out how many quarter turns the man must rotate through to look like each of the pictures.
An odd version of tic tac toe
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
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?
Move just three of the circles so that the triangle faces in the opposite direction.
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?
Exchange the positions of the two sets of counters in the least possible number of moves
A variant on the game Alquerque
How many different rhythms can you make by putting two drums on the wheel?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?