SOLUTION: How many spheres of radius 1cm can you place inside a equilateral triangular pyramid of side 10cm

Question 385852: How many spheres of radius 1cm can you place inside a equilateral triangular pyramid of side 10cm
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
I'll assume that the spheres must take their own shape, without being altered.
I would imagine the answer being (4+3+2+1) + (3+2+1) + (2+1) + 1 = 20, obtained by starting with a triangle of spheres with 4 spheres to a side, and letting the side length go to 3, 2, 1. I'm not quite sure how to prove this...it'll definitely require much higher level mathematics.
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