By how much can a leaning column made of 1,000,000 rigid bricks overhang over a cliff?

Question

The bricks are stacked on top of each other on the edge
of a cliff, no glue. Each brick has dimensions 2" x 5" x 10"

Think a stack of books.

Answer 1

The overhang can be found by the following:

(1/2)H(1000000)(10 inches)

where H(n) is the nth Harmonic number. As an approximation, we can use:

(1/2)(Log(1000000) + 0.577215)(10) = 74.8497 inches

The divergent series sum ∑(1/n) does approximate the logarithmic function. Meanwhile, the stack would be over 31.56 miles high, so that due to the curvature of the Earth, the effective overhang relative to the ground would be reduced to 74.0377 inches.

Answer 2

Crunch the numbers yourself,

Am. J. Phys. 73(12) 1107 (2005)
DOI:10.1119/1.2074007

http://mathworld.wolfram.com/BookStackingProblem.html
http://theory.lcs.mit.edu/classes/6.042/fall06/lec12.pdf
http://pdf.aiaa.org/preview/1993/PV1993_3933.pdf
http://en.wikipedia.org/wiki/Block_stacking_problem