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Broad Topics > Numbers and the Number System > Triangle numbers

Light the Lights Again

Stage: 2 Challenge Level:

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?

Handshakes

Stage: 3 Challenge Level:

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

Mystic Rose

Stage: 3 Challenge Level:

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

Triangle Numbers

Stage: 3 Challenge Level:

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

Route to Infinity

Stage: 3 and 4 Challenge Level:

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

Factors and Multiples Puzzle

Stage: 3 Challenge Level:

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

Take Ten Sticks

Stage: 3 and 4 Challenge Level:

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?

Picturing Triangle Numbers

Stage: 3 Challenge Level:

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

Slick Summing

Stage: 4 Challenge Level:

Watch the video to see how Charlie works out the sum. Can you adapt his method?

Speedy Summations

Stage: 5 Challenge Level:

Watch the video to see how to add together an arithmetic sequence of numbers efficiently.

Reasonable Algebra

Stage: 4 Challenge Level:

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

A Square Deal

Stage: 2 Challenge Level:

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

Graphing Number Patterns

Stage: 2 Challenge Level:

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?

Iff

Stage: 4 Challenge Level:

Prove that if n is a triangular number then 8n+1 is a square number. Prove, conversely, that if 8n+1 is a square number then n is a triangular number.

Sam Again

Stage: 3 Challenge Level:

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.

Man Food

Stage: 2 and 3 Challenge Level:

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?

Cat Food

Stage: 2 Challenge Level:

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?

Forgotten Number

Stage: 3 Challenge Level:

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

Reciprocal Triangles

Stage: 5 Challenge Level:

Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.

Alphabet Blocks

Stage: 1 and 2 Challenge Level:

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?