In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

How many possible necklaces can you find? And how do you know you've found them all?

Can you work out how to win this game of Nim? Does it matter if you go first or second?

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out the missing numbers?

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

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?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

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.

Investigate and explain the patterns that you see from recording just the units digits of numbers in the times tables.

Can you make arrange Cuisenaire rods so that they make a 'spiral' with right angles at the corners?

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

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? What do you think is happening to the numbers?

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

Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?