[extropy-chat] Puzzle - Short Tale

[Spike]

> Can anyone answer this?
> 
> A monk wakes one morning and decides to climb the mountain 
> next to his hut...  Prove your answer... Natasha

*Thank* *You* *Natasha* for that cool puzzle.  Since
it is fair game to post math puzzles, do indulge me
with one that has been driving me nuts for days, a
slap-in-the-face evidence that I was *smarter* when
I was a 19 yr old divinity student than I am now, a
43 yr old extropian.

The book of John describes the apostles fishing all
night and coming up empty.  Jesus or Hoerkheimer (unclear
which one) showed up and told them to cast the net again.
Chapter 21 verse 11 readeth:  "Simon Peter went up, and
drew the net to land full of great fishes, an hundred and
fifty three: and for all there were many, yet was not the
net broken..."

Matthew 12:36 declareth "...every idle word that men 
shall speak, they shall give account thereof in the 
day of judgement."

That day of judgement will be one looooong afternoon,
my friends, but clearly the bible contains *no idle 
words* so why did god specifically tell us that there
were 153 fish in that net?  What is special about 153?

I found an old notebook in which I used to do mathematical
puzzles.  I had found in a commentary that 153 is the smallest
number that is equal to the sum of the cubes of its digits.
I do vaguely recall doing the calcs that resulted from my
musing "What are the other numbers that are the sum of
the cubes of their digits?"

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-[  

Help me Obi wan Extropi, you're my only hope.  

spike