Forum: Community Center


Subject: Community Center Forum Carnival Booth

Wolfenshire opened this issue on May 28, 2024 · 128 posts


3dcheapskate posted Mon, 03 June 2024 at 4:38 AM

I think the jar of marbles (first tier) contains 135 marbles

Do I get extra kudos for including my working out ? If so, here goes:
Assume the marbles are (a) all of an equal size, and (b) they adopt an HCP (Hexagonal Close Packed) crystal lattice structure within the jar.
At its widest the jar seems, from visual inspection, to be able to hold a horizontal layer containing a maximum of four marbles in a straight line giving. So assuming a planar hexagonal array with a 2-3-4-3-2 configuration*, this would give 14 marbles per layer.
From visual inspection it would appear that the jar can contain five of these layers plus smaller intermediate layers between each pair of layers, and since the jar is tapered at the top and bottom there will be smaller layers above the uppermost layer and below the lowermost layer - thus six intermediate layers.
The intermediate layers would adopt a 2-3-4-3** configuration for 12 marbles per layer.
This gives a total of 5×14+6×12=142 marbles (or the smaller alternative* of 125 marbles)
Another visual inspection indicates that the marbles do not appear to have been placed in an HCP lattice, so we can ignore all this and just make a random guess

*Alternatively a 1-4-3-4-1 configuration for the main layers would only give only 13 marbles per layer, and would allow a 2-3-2-3 configuration for intermediate layers of 10 marbles each, which gives a total of 5×13+6×10=125 marbles

**The intermediate layers can extend beyond the main layers as long they do not extend beyond the constraining inner wall of the glass jar.



The 3Dcheapskate* occasionally posts sensible stuff. Usually by accident.

*also available in ShareCG, DAZ, and CGBytes flavours.