[extropy-chat] Puzzle - Short Tale

[Alejandro Dubrovsky]

On Fri, 2004-02-06 at 14:05, Spike wrote:
> At the time I had a counterfeit Apple, but no printer,
> (and no sense of guilt for the theft of Apple's 
> intellectual property) so if I calculated something, I 
> had to write it down in a notebook.  Usually I also wrote 
> down the algorithm but this time I wrote only the damn answers
> and Im going crazy trying to figure out how I figured
> this out 24 yrs ago with a 3.2 megahertz computer.  Yes
> young people, they really did go that slow back then.  
> 
> I wrote a couple pages of cryptic notes and figures,
> interspersed with the numbers 370, 371 and 407.  These
> are numbers that are the sum of their cubes.
> 
> A few pages over I wrote "numbers equal to the 4th power
> of their digits:  1634, 8208, 9474."
> 
> Later a table:
> 
> 5th power:  4150, 4151, 54748, 92727, 93084, 194979.
> 
> 6th:  548834
> 
> 7th:  1741725, 4210818, 9800817, 9926315, 14459929.
> 
> 8th:  24678050, 24678051, 88593477
> 
> I neglected to write down the algorithm!  Question please, 
> before I go crazy, HOW COULD I have found those solutions?
> I do vaguely recall deriving the code, but now Im at a
> complete loss for how.  OH NO I've grown stuuuupiiiiid!  {8-[  
> 
You probably stored partial results for each number you calculated,
since 548834 is just the result for 48834 plus the result for 5.  On
that old machine you probably would have run out of memory pretty
quickly but you could have most likely stored all three digit numbers,
and then worked with those.  Your 8 digit numbers could have been done
in a 3x3x2 combination which would be 100 million calculations at two
additions each plus a comparison.  Each addition and comparison could
have taken a while (you'd had have to have written your own adding
algorithm to add 32 bit numbers) so give it 20 cycles (would that have
been enough?), which puts total at 6 billion cycles, or a bit over half
an hour. 
If you could have stored all 4 digit numbers (but that would take 40k),
it would have cut down a third of the steps (one less addition to get to
8 digit).  Does that sound about right or was it much faster?
alejandro