Choose four of the numbers from 1 to 9 to put in the squares so
that the differences between joined squares are odd.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you hang weights in the right place to make the equaliser
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Place six toy ladybirds into the box so that there are two
ladybirds in every column and every row.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
If you have only four weights, where could you place them in order
to balance this equaliser?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?
Can you use the numbers on the dice to reach your end of the number line before your partner beats you?
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....?
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?
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?
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!
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
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Choose a symbol to put into the number sentence.
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?
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?
Use the number weights to find different ways of balancing the equaliser.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
Find out how we can describe the "symmetries" of this triangle and
investigate some combinations of rotating and flipping it.
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Use the clues to colour each square.
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?
An odd version of tic tac toe
Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
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?
How many different rhythms can you make by putting two drums on the
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
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?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
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?
Can you find all the different ways of lining up these Cuisenaire
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?
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
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?
Investigate the different sounds you can make by putting the owls
and donkeys on the wheel.