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I guarantee you: the toughest riddle you've seen in a while!

 
 
Reply Thu 5 Jan, 2006 10:52 pm
Or 100% money back. It's a number sequence.

8
11
94
58
10
49
57
404
1272
8699
3292
3332
48033
90311
112817
1149731
24909936
1838500
5264650
29232231
76236585
64535680
49758988
191873638
1718045848 (this one took 6 minutes to compute)
...

I realize this is a toughie so here are some hints/specifics:

1. I chose to start it at 8 for convenience, but any number will work. Be wary though, certain numbers get the sequence into a loop.

2. Each number in the sequence is represented in two ways: as a string and as a number. Each following term is derived by considering the chosen term as a string, and the next term as a number (and then applying a certain algorithm of course). For example, the string "0319" has a corresponding next numeric term (which happens to be 23149), but it has no previous term (unless you're willing to let the numerical representation be 319, but that's cheating). Therefore, not all strings (ones that begin with a 0) can be in the sequence, but (I think) all numbers can.

3. The numbers get progressively harder and harder to compute, but there IS the possibility of it "collapsing" back to a small number (such as 192 or something), or even going back to the original number (thus going into a loop).

4. At first I chose 0 as the first number. Then I entered the sequence into Google to make sure you couldn't get it from there. You can. So I used 8.

That should be plenty of hints. In case you want to know, it took me 6 minutes to compute the last term using a computer program. Actually, programming abilities and a certain text file (you will need some outside information) are highly recommended, but if you knack your brains and try everything, you stand a chance too.

Have...err...fun! Razz
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markr
 
  1  
Reply Thu 5 Jan, 2006 11:00 pm
So, the number 11 is derived from the string representing 8, correct?
0 Replies
 
TechnoGuyRob
 
  1  
Reply Thu 5 Jan, 2006 11:01 pm
Correct.

"8" => 11
"11" => 94
...
0 Replies
 
markr
 
  1  
Reply Thu 5 Jan, 2006 11:30 pm
"certain text file"

ASCII chart?
Morse code table?


"8" => 11
and not
"eight" => 11
correct?
0 Replies
 
TechnoGuyRob
 
  1  
Reply Fri 6 Jan, 2006 06:58 am
ASCII chart?
Morse code table?

Pure .txt file, which looks the same (although its size/extent may differ) no matter what the format. Of course with Google you can find an acceptable tool too.

And yes, "8" not "eight".
0 Replies
 
markr
 
  1  
Reply Fri 6 Jan, 2006 10:48 am
Got it. I don't care to take the time to compute the next number, but if you had started with 4, the first five terms of the sequence would be:
[size=7]4, 2, 6, 7, 13[/size]
0 Replies
 
TechnoGuyRob
 
  1  
Reply Fri 6 Jan, 2006 03:36 pm
Nice job! I have to say, I'm impressed. Too many hints? Razz
0 Replies
 
markr
 
  1  
Reply Fri 6 Jan, 2006 11:00 pm
Thanks. I don't think there were too many hints. Hints 1, 3, and 4 weren't really helpful. The "text file" hint helped, but I started down the wrong track. I tossed and turned last night trying to find a way to map 8 to 11 (ASCII code, morse code, etc.).

The comment about getting harder to compute threw me off a bit. I assumed it was based on a computational (not search) algorithm that took more time as the numbers grew larger.

In the shower this morning (before I saw your response to my last question), I got to thinking that it could be based on a search, but my first thought was it could be any famous text. Then pi popped into my head.

I think I had an advantage because I've thought about constructing sequences based on the digits of pi or e. Here's a similar one for you that I just made up:
4, 1, 9, 6, 8, 7, 3, 4, 4, 7

and another:
1, 1, 4, 1, 9, 5, 7, 2, 8, 9

and another:
1, 5, 3, 2, 3, 4, 1, 3, 8, 9
0 Replies
 
 

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