Three.

Click the image to build a Pyramid

Let us use three-sided pyramids (sometimes called tetrahedrons). To make the pyramid, start with a triangular arrangement of tennis balls for the bottom layer. Next stack up tennis balls layer at a time.

If the base of the pyramid has 5 balls along a side,
how many balls does the entire pyramid have in it?
This is a **pyramidal number**.

Here is a chart that shows the number of balls in the side of a base,
**N**,
and the corresponding pyramidal numbers.
Assume that a single tennis ball counts as a pyramid of side one, so Pyramid(1) is 1.

The picture starts with the base of the pyramid for **Pyramid(5)**.
Click a few times to see the complete pyramid.
Smaller pyramids can be found within this one.
(For example, the top two layers can be considered a pyramid that has a base
with two balls on a side.)
For small pyramids, count the balls within them.
Try to find a clever way to
calculate **Pyramid(N)**.

Click on the image a few times and fill in some of the chart.