RE: [MLUG - DISCUSSION] beginner slide rule wanted

[Jonathan King <EMAIL:PROTECTED>]

On Wed, 2 Jul 2003, Mike Miller wrote:

> On Wed, 2 Jul 2003, Mike Miller wrote:
> 
> > > So every year I walk students through the Tower of Hanoi Problem with a
> > > small number of disks, establish that the number of moves it takes for
> > > the n disk problem is 2^n - 1, and then ask for people to guess how long
> > > the 64 disk problem takes if you can do 1 move per second.
> >
> > I do it as (2^10)^6 * 2^4 which more than 16*(10^3)^6 = 1.6*10^19 seconds.
> > But how long is that?  There are 3600 seconds per hour and 24 hours per
> > day so there are about 8.6*10^5 seconds per day and about 3.7*8.6*10^7 or
> > 3.2*10^8 seconds per year.  So that means (1.6/3.2)*10^(19-8) = 5 x 10^10
> > days to solve.  That is 50 billion.
> 
> And I screwed up at the end.  Meant to say 5 x 10^10 *years* to solve, or
> 50 billion years.

Alas, that wasn't your only error.  3600*24 < 10^5.  Repeat after me: 
there are pi*10^7 seconds in a year, approximately.  This is well-worth 
remembering both for problems like this, and for times when you get an 
answer that says you'll need some non-trivial fraction of a year of CPU 
time or the like.

So if 2^64 = 16*10^18 (for exactly the reason you say), the answer 
we're looking is 16*10^18 / (# of years in a second) = 5.something * 10^11
years. So you're off by a factor of 10.
 
> Doing it with a computer, I get 58.4 billion years, which doesn't bother
> me because I knew I was low and I was shooting mostly for the order of
> magnitude.

Well, it bothers me since your computer has slipped a place. :-)

jking


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