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.
A Mystic Rose is a beautiful image created by joining together points that are equally spaced around a circle.
Watch the animation below to see how a Mystic Rose can be constructed. You can change the number of points around the circle.
Whose method do you prefer?
How many lines are needed for a 100 pointed Mystic Rose?
Could there be a Mystic Rose with exactly 4851 lines?
Or 6214 lines?
Or 3655 lines?
Or 7626 lines?
Or 8656 lines?
How did you decide?
You may wish to try the problems Picturing Triangle Numbers 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.
Click here for a poster of this problem.