Can you hang weights in the right place to make the equaliser balance?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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 10 in the circles so that each number is the difference between the two numbers just below it.

Use the number weights to find different ways of balancing the equaliser.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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.

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

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?

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?

Can you use the numbers on the dice to reach your end of the number line before your partner beats you?

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?

If you have only four weights, where could you place them in order to balance this equaliser?

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Can you find all the different ways of lining up these Cuisenaire rods?

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?

How many different rhythms can you make by putting two drums on the wheel?

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?

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!

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?

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

Can you complete this jigsaw of the multiplication square?

What happens when you try and fit the triomino pieces into these two grids?

Use the interactivities to fill in these Carroll diagrams. How do you know where to place the numbers?

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?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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?

How many different triangles can you make on a circular pegboard that has nine pegs?

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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?

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?

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.