Resources tagged with: Triangle numbers

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There are 21 results

Broad Topics > Properties of Numbers > Triangle numbers

Human Food

Age 7 to 14
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?

Sam Again

Age 11 to 14
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.

Summing Consecutive Numbers

Age 11 to 14
Challenge Level

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?

Picturing Triangular Numbers

Age 11 to 14
Challenge Level

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

Triangular Triples

Age 14 to 16
Challenge Level

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

Hot Pursuit

Age 11 to 14
Challenge Level

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...

Series Sums

Age 14 to 16
Challenge Level

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

Slick Summing

Age 14 to 16
Challenge Level

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

Triangle Numbers

Age 11 to 14
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?

Handshakes

Age 11 to 14
Challenge Level

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

Mystic Rose

Age 14 to 16
Challenge Level

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

Triangles Within Squares

Age 14 to 16
Challenge Level

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

Clever Carl

Age 7 to 14

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.

Triangles Within Triangles

Age 14 to 16
Challenge Level

Can you find a rule which connects consecutive triangular numbers?

Triangles Within Pentagons

Age 14 to 16
Challenge Level

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

Route to Infinity

Age 11 to 14
Challenge Level

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

Take Ten Sticks

Age 11 to 16
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?

Factors and Multiples Puzzle

Age 11 to 14
Challenge Level

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

Satisfying Statements

Age 11 to 14
Challenge Level

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

Forgotten Number

Age 11 to 14
Challenge Level

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

Iff

Age 14 to 18
Challenge Level

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