I've wondered before about a little toy problem, and I think I've solved it, but just to be sure, I'll let you guys have it and see what you get. Alright, so you have a table and a (possible infinite) stack of circular disks of radius R and of neglible thickness (each disk is identical, having uniform density and mass M). Say you take one disk, and put it so that a little bit is hanging off the side of the table. Clearly, if you move it so that more than half of it is off the table, it will fall. However, by moving it back just a little and adding a second disk, you can extend its "reach" a little further. By moving these back in the right proportions and adding a third disk, you can extend it a little further. The question is what is the maximum range of stacked disks? For the case when higher-up disks have to be strictly to the right of lower disks, I got that the maximum reach is simply R. I haven't solved it for the general case of arbitrary stackings of disks, but I suspect that if one is allowed to stack them arbitrarily, you can get arbitrarily far away from the table. However, I also wonder how the problem changes if you include things like friction? And what if you only have a fixed finite number of disks? Any thoughts would be greatly appreciated. I have another one involving springs if you guys like this one.