20071020, 06:48  #1 
Sep 2007
17 Posts 
Numbers in Tables : Part 2
(Before you read this, you better read the former thread, in this forum, under the same tittle)
Continuing the first thread, now I'll give you more tables that are filled with numbers only 1 to 40, so it won't much hurt your eyes. Thus many rows are blank. I put the file in .xls format (Windows XP) at: http://www.artofproblemsolving.com/F...c.php?t=171338. Tables 120 in sheet #1 & #2, are same as before and have been corrected some (of mistyping), Tables 2132 in sheet #3, Tables 3344 in sheet #4,...,Tables 273284 in sheet #24. I name and arrange the tables just like that, though you can do else. HAPPY PUZZLING.. http://www.artofproblemsolving.com/F...ops/spacer.gif Last fiddled with by wustvn on 20071020 at 06:56 
20071020, 07:36  #2 
"Lucan"
Dec 2006
England
14512_{8} Posts 

20071106, 12:00  #3 
Sep 2007
17 Posts 
The clues of this thread had been written at:
http://www.ocf.berkeley.edu/~wwu/cgi...num=1192863624 
20071118, 08:24  #6 
Sep 2007
17 Posts 
I need to write again here what I’ve been doing to this puzzle, though this had been written partly in other forum. I assume you guys have seen the file sept09A.xls.
I’m not a puzzle mania, this puzzle just disturbs my mind. So to those whoever interested in this puzzle, I THINK the tables in my explanation below are the “keys” of this puzzle because: 1).Their shapes are quite different from other tables, where numbers 1 to 40 are only in certain rows. Especially in Table 45, numbers 1 to 40 are only in rows 1 & 10. (This can also approve that this is not a random case. Do you guys agree with that?). Meanwhile for other tables, numbers 1 to 40 spread almost in rows 1 to 10. 2).These tables have similar shapes each other. E.g: Table 45 has similar shape with Table 49 & Table 53. Table 57 has similar shape with Table 61 & Table 65. Here below I think tables that have similar shapes: 45,57,69,81,93,105,117,129,141,153,165,177,189,201,213,225,237,249,261,2 73. with 49,61,73,85,97,109,121,133,145,157,169,181,193,205,217,229,241,253,265,2 77. and 53,65,77,89,101,113,125,137,149,161,173,185,197,209,221,233,245,257,269, 281. These tables “themselves” look similar. E.g: Table 49 looks similar with Table 169. Table 73 looks similar with Table 193. Here below I think tables look similar: 49,73,97,121,145,53,77,101,125,149,57,81,105,129,153,61,85,109,133,157,6 5,89,113,137,161,69,93,117,141,45 with 169,193,217,241,265,173,197,221,245,269,177,201,225,249,273,181,205,229, 253,277,185,209,233,257,281,189,213,237,261,165 Next time I’ll try to explain more details about the gray areas (my approaching method) as shown in Table 1, sheet #1, file sept09A.xls. Yeah, for its big sizes, this puzzle is really tough. Needs geniuses to crack it, at least above averages… 
20071126, 19:15  #7 
Just call me Henry
"David"
Sep 2007
Cambridge (GMT/BST)
2^{2}×3×5×97 Posts 

20071127, 01:28  #8 
Jun 2003
2^{3}×607 Posts 
The puzzle looks like it is just giving the position of various digits in a string of digits (perhaps some kind of special numbers). It just looks arbitrary.

20071129, 17:27  #9 
Feb 2007
2^{4}×3^{3} Posts 
IS there a (deterministic) rule according to which the numbers are placed ?
Or are the only rules the monotonic growth of each list, and the "unique" position of each number in each table ? i.e. the requirement that each number appears exactly once in each table, and that (if I understood well) if the number X occurs at position N in the list L of table T, then it may not occur at position N in the list L of any other table ? Is this the correct and complete specification of the requirement ? I think this allows for an infinity of solutions, and even knowing ONE solution filled up to N=350, it does not determine that solution for the N>350 e.g. you can just fill the first table as you want, and make different permutations for the other tables. 
20071231, 05:14  #10 
Sep 2007
17 Posts 
I'm so sorry for being late to answer you guys, because I'm handling so many forums where I put this puzzle.
In EACH tables, each numbers appears just one time and there will be no same numbers vertically, horizontally and diagonally. If the number X occurs at position N in the list L of table T, then it may occur at position N in the list L of any other table. Thank's. 
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