Triangle numbers

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

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.
problem

Reciprocal Triangles

Age

16 to 18

Challenge level

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

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.
problem

Series Sums

Age

14 to 16

Challenge level

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

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...
problem

Alphabet Blocks

Age

5 to 11

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?
problem

Swimming Pool Tiles

Age

7 to 11

Challenge level

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

Cat Food

Age

7 to 11

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?
problem

Graphing Number Patterns

Age

7 to 11

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?