Posted by Keira on Saturday, June 27, 2009 at 11:39am.
http://en.wikipedia.org/wiki/Tetrahedral_number
look at the rotating triangular pyramids and count the number of balls for the different layers
top layer: 1 ball
top two layers: 4 balls
top three layers: 10 balls
etc.
you can figure out the number of balls for any number of layers n by
n(n+1)(n+2)/6
e.g. if n=3
3(4)(5)/6 = 10
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