01 Nov '05 20:091 edit

Suppose you have n circular coasters, a table, and a lot of free time. What is the maximum table overhang you can acheive by stacking the coasters on the edge of the table? You may assume that each of these coasters:

1) has unit mass;

2) has unit diameter;

3) is weighted so that its centre of gravity runs directly through its geometric centre; and

4) is infinitely strong, so that is does not deform under stacking stresses.

To get started, what is the maximum table overhang for:

a) 1 coaster?

b) 2 coasters?

c) 3 coasters?

d) 10 coasters?

And what is the maximum table overhang you can acheive given an infinite number of coasters? (Drinking games will never be the same again!!)

1) has unit mass;

2) has unit diameter;

3) is weighted so that its centre of gravity runs directly through its geometric centre; and

4) is infinitely strong, so that is does not deform under stacking stresses.

To get started, what is the maximum table overhang for:

a) 1 coaster?

b) 2 coasters?

c) 3 coasters?

d) 10 coasters?

And what is the maximum table overhang you can acheive given an infinite number of coasters? (Drinking games will never be the same again!!)