Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?

Sam displays cans in 3 triangular stacks. With the same number he could make one large triangular stack or stack them all in a square based pyramid. How many cans are there how were they arranged?

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

This activity creates an opportunity to explore all kinds of number-related patterns.

Here is a collection of puzzles about Sam's shop sent in by club members. Perhaps you can make up more puzzles, find formulas or find general methods.

I added together the first 'n' positive integers and found that my answer was a 3 digit number in which all the digits were the same...

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

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?

Can you find any two-digit numbers that satisfy all of these statements?

What would you do if your teacher asked you add all the numbers from 1 to 100? Find out how Carl Gauss responded when he was asked to do just that.

Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?

Take a look at the multiplication square. The first eleven triangle numbers have been identified. Can you see a pattern? Does the pattern continue?

I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...

Can you describe this route to infinity? Where will the arrows take you next?

Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?

Take ten sticks in heaps any way you like. Make a new heap using one from each of the heaps. By repeating that process could the arrangement 7 - 1 - 1 - 1 ever turn up, except by starting with it?