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There are **29** NRICH Mathematical resources connected to **Triangle numbers**, you may find related items under Properties of numbers.

Problem
Primary curriculum
Secondary curriculum
### Light the Lights Again

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Slick Summing

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Handshakes

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Mystic Rose

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

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Route to Infinity

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Factors and Multiples Puzzle

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Take Ten Sticks

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?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Picturing Triangular Numbers

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Iff

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Age 14 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Summing Consecutive Numbers

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Swimming Pool Tiles

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Satisfying Statements

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Speedy Summations

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles Within Pentagons

Show that all pentagonal numbers are one third of a triangular number.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles Within Squares

Can you find a rule which relates triangular numbers to square numbers?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangles Within Triangles

Can you find a rule which connects consecutive triangular numbers?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Clever Carl

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.

Age 7 to 14

Problem
Primary curriculum
Secondary curriculum
### A Square Deal

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Graphing Number Patterns

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Triangular Triples

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Hot Pursuit

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...

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sam Again

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Human Food

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?

Age 7 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cat Food

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Series Sums

Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Forgotten Number

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reciprocal Triangles

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

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Alphabet Blocks

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?

Age 5 to 11

Challenge Level