Resources tagged with: Triangle numbers
There are 29 NRICH Mathematical resources connected to Triangle numbers, you may find related items under Properties of numbers.
Broad Topics > Properties of numbers > Triangle numbers
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?
Slick Summing
Watch the video to see how Charlie works out the sum. Can you adapt his method?
Handshakes
Can you find an efficient method to work out how many handshakes there would be if hundreds of people met?
Mystic Rose
Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.
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?
Route to Infinity
Can you describe this route to infinity? Where will the arrows take you next?
Factors and Multiples Puzzle
Using your knowledge of the properties of numbers, can you fill all the squares on the board?
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?
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?
Iff
Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?
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?
Swimming Pool Tiles
This activity creates an opportunity to explore all kinds of number-related patterns.
Satisfying Statements
Can you find any two-digit numbers that satisfy all of these statements?
Speedy Summations
Watch the video to see how to add together an arithmetic sequence of numbers efficiently.
Triangles Within Pentagons
Show that all pentagonal numbers are one third of a triangular number.
Triangles Within Squares
Can you find a rule which relates triangular numbers to square numbers?
Triangles Within Triangles
Can you find a rule which connects consecutive triangular numbers?
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.
A Square Deal
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
Triangular Triples
Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.
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...
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.
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?
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?
Series Sums
Let S1 = 1 , S2 = 2 + 3, S3 = 4 + 5 + 6 ,........ Calculate S17.
Forgotten Number
I have forgotten the number of the combination of the lock on my briefcase. I did have a method for remembering it...
Reciprocal Triangles
Prove that the sum of the reciprocals of the first n triangular numbers gets closer and closer to 2 as n grows.
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?