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.
Well done Amelia and Kahlia from Ardingly College, Lauren from St. Matthew's School and Kate from Orston Primary for realising that the pattern would continue indefinitely.
Kahlia reminded us that
Lauren noticed that:
And Kate noticed that:
So that clarifies why we go down from one triangle number to another along odd numbered columns when the difference between the triangle numbers is odd.
So, moving across adds the next even number, moving down adds the next odd number: