Quandaries and Queries
When stacking oranges to form a triangular pyramid, each orange touching 3 oranges below it. In order to have a pyramid with 6 layers, how many oranges should be on the bottom layer?
I didn't have any oranges so I used apples, macintosh apples from British Columbia.
Here is a triangular pyramid of apples with 1 layer.
Here is one pyramid with 2 layers
and one with 3 layers.
What you need to notice is that to go from the triangular base for the 2 layer pyramid
to the triangular base for a 3 layer pyramid
you add one row of apples along a side of the triangle.
How many apples will you need for the triangular base for a 4 layer pyramid?