I have forgotten the number of the combination of the lock on my
briefcase. I did have a method for remembering it...
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?
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.
Triangle numbers can be represented by a triangular array of squares.
Imagine two copies of a triangular array of squares. Can you picture how to fit them together to make a rectangle? What is special about the dimensions of your rectangle?
Use the activity below to test your ideas.
Which are triangle numbers?
How did you decide?
Do any triangle numbers end $000$?
You may wish to try the problems Mystic Rose and Handshakes. Can you
see why we chose to publish these three problems together?
You may also be interested in reading the article Clever Carl, the story of a young mathematician who came up with an efficient method for adding lots of consecutive numbers.