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Two happy ends (Posted on 2011-03-07) Difficulty: 3 of 5
Consider a series of numbers, defined as follows:
Starting with any natural number, each member is a sum of the squares of the previous member`s digits.

Prove : The series always reaches either a stuck-on-one sequence: 1,1,1 or a closed loop of the following 8 numbers: 145,42,20,4,16,37,58,89, ...

Ex1: 12345,55,50,25,29,85,89,145.. etc
Ex2: 66,72,53,34,25,29,85,89,145
Ex3: 91,10,1,1,1..

See The Solution Submitted by Ady TZIDON    
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re(5): NOT enough by Gamer | Comment 7 of 11 |
(In reply to re(4): solution NOT enough by Gamer)

I did not want to start a chain of unnecessary remarks, which do not focus on the solution , but on "who said what "and "what  was his intention".

Allow me to present the facts re Jer's and Charlie's posts,
which you, Gamer without any justification combined into a joint solution in addressing my short remark to Jer, which I quote':

" Whatever you said is true, but you did not prove that there are only two possibilities : a  loop of 1,1.. and  the closed loop of 8  specific numbers.

Which means:" ..You're totally right, but you did not provide a solution, you provideed an outline of solution, a solution enough.
We still do not know how many cycles exist. "

On various occasions I do the same: either provide a short synopsis of the way to solve or provide just the answers without
further explanation. Nothing wrong with this.

There was no need to rush to Jer's defence stating
" seems like your solution is the same as Charlie's -- the only thing you left out is the program " etc 

That is wrong :

 "your solution is the same as Charlie's "    NO, SIR

Jer spoke about strategy and was not interested in the result.
Charlie solved the issue in full, even providing the distribution  between the two happy endings.
Jer understood that only 99 (and not 999 ) numbers have to be examined (need I explain WHY?) , Charlie did not give too much thoughts in this regard.

I hope that in the future your remarks (always welcomed) will be posted after giving them more serious

Please feel free to Email me, if you think it's needed.

  Posted by Ady TZIDON on 2011-03-09 07:17:33
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