364 physics/brick.p
Description
This article is from the Puzzles FAQ, by Chris Cole chris@questrel.questrel.com and Matthew Daly mwdaly@pobox.com with numerous contributions by others.
364 physics/brick.p
What is the maximum overhang you can create with an infinite supply of bricks?
physics/brick.s
You can create an infinite overhang.
Let us reverse the problem: how far can brick 1 be from brick 0?
Let us assume that the brick is of length 1.
To determine the place of the center of mass a(n):
a(1)=1/2
a(n)=1/n[(n-1)*a(n-1)+[a(n-1)+1/2]]=a(n-1)+1/(2n)
Thus
n 1 n 1
a(n)=Sum -- = 1/2 Sum - = 1/2 H(n)
m=1 2m m=1 m
Needless to say the limit for n->oo of half the Harmonic series is oo.
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