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

This big box adds something to any number that goes into it. If you know the numbers that come out, what addition might be going on in the box?

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 1-5 in the V shape so that both 'arms' have the same total?

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

In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?

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!

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?

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?

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

This challenge is about finding the difference between numbers which have the same tens digit.

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.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

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?

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

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?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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.

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?

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?

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?

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

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

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?

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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?

Can you make square numbers by adding two prime numbers together?

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

Here is a chance to play a version of the classic Countdown Game.

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

An environment which simulates working with Cuisenaire rods.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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.

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.

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.

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

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?