This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Explore Alex's number plumber. What questions would you like to ask? Don't forget to keep visiting NRICH projects site for the latest developments and questions.

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

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!

Use the information about Sally and her brother to find out how many children there are in the Brown family.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

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

You have 5 darts and your target score is 44. How many different ways could you score 44?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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?

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!

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Suppose there is a train with 24 carriages which are going to be put together to make up some new trains. Can you find all the ways that this can be done?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

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?

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

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

These two group activities use mathematical reasoning - one is numerical, one geometric.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

Investigate what happens when you add house numbers along a street in different ways.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

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?

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.

Find all the numbers that can be made by adding the dots on two dice.

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?

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?