OK, it's time to reveal in two parts what I know about the Champagne Pyramid Trick.
First you have to have a stable formation, a tetrahedron or triangular pyramid that will use up 680 wine glasses. This is a lot harder than it sounds. I did a little by trial and error:
1. I looked at an extended bowling pin arrangement and discovered that with 15 glasses in the bottom triangle the total in the stack of having one less in each ascending row would be 666. Unless a square pattern fits better (which as you will see in #2 is not the case)you have to add glasses into the formation somewhere, which is one for each level except the top one (which has to be just 1)
2. You must switch to a square pattern and start the same way with a level 1 square of 9 x 9. Level 2 is 8x8, 64. Level 3 is 7x7, 49. Level 4 is 6x6, 36. Level 5 is 5x5, 25. level 6 is 4x4, 16, level 7 is 3x3, 8. level is 2x2, 4. level 9 is 1. Add them up quickly and you get 819, so level 1 must start with 12 and not 13. then you add them up to get 650. You can't get there from here on this one either.
3. A hybrid approach appears the only one that can work but I have to back off and say that the mathematical closure on this just isn't there. My mistakes in the earlier two approaches led to inaccurate conclusions, but I hope you had some fun trying out your mathematical dexterity. If anyone did better let's hear about it.
The other side of the equation is how to actually stack the glasses. Heresay has it that if you take out one glass from most many levels, the champagne will be able to drain through there. Here is what a professional bartender who has done this trick has been reported about the proper way to do it:
You know that the glasses have to be stacked in a pyramid.
Now here's the trick to filling all the glasses and not pouring your Champagne all over the table top....make sure your glasses are about a fingers width apart all around. If they're touching each other, the Champagne will follow the rims and stems and just dribble all over the place(not good). By keeping the glasses from touching each other, the Wine will follow the stems and bases of the glass just like the little waterfall you want to have.
You won't even need a tray under glasses. No wine will wet the table as long as the glasses are not touching each other.
No doubt there will be those dissatisfied with this analysis. I say you should go out and buy 660 wine glasses and try it out.
I expect all of you will enjoy this demonstration of a tetrahedron shape with about 5000 glasses, which is totally amazing:http://www.metacafe.com/watch/343130/pyramid_of_glasses/
Try it at your next party.