Triangle numbers

There are 30 NRICH Mathematical resources connected to Triangle numbers

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

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?

problem

Favourite

Route to infinity

Age

11 to 14

Challenge level

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

problem

Favourite