Reaper wrote:Alright, let me take a stab at this one.
If you layer 10x10 = 100 balls.
next layer will be between the other balls, now the question is what percent you take the ball sinks lower. Gonna take 33%.
new layer is now 9x9 = 81 balls but you gain 33% space per 1cm layer.
so, 181 balls per 1.66cm layer.
5cm / 1.66cm = 3
3 * 181balls = 543 balls
Your first layer is stacked 10x10... interesting.
have you considered stacking your first layer in the following format:
10 then 9 then 10 then 9 then 10 then 9 then 10.... doing it that way, means you can fit in an extra row on the bottom layer thereby increasing the total bottom layer to 105 balls instead of the 100 you've mentioned. The question is what do you do with the second layer... ;-)
By the way, the mathematics to calculate the height of a second layer is quite cool in it's own right (you just "assumed" 33%). I.e. 2 balls on the bottom layer with the top layer inbetween. Versus 3 balls in a triangle shape on the bottom with the second layer lying inbetween the 3 balls, versus 4 balls in a square with the top layer sitting between them. The really cool one to calculate is if you have 5 balls in a ring shape on the bottom and you put the second layer on top of that one. As a matter of interest, if you have 6 balls on the bottom layer making a ring, then the space in the middle is big enough for a ball to actually sit inside the middle.
But no, short answer, I have calculated a much bigger number than what you and Morhp have thusfar came up with.