20191114, 23:37  #34 
Sep 2017
2^{2}×3×7 Posts 
Signing off

20191114, 23:59  #35 
"Hugo"
Jul 2019
Germany
31 Posts 
From where do you take the conviction that there is no shortcut? I do not know if you should call it a shortcut, if someone realizes what I said a few posts above with "Much more promising would be good ideas regarding a structure of the matrices."?
I've been wondering if I should give this information here, but normally the puzzle team at IBM should have already provided an update to the website. I am rather disappointed because no feedback on the state of the competition is visible and the idea with the *awards does not fulfill the purpose as I had imagined. 
20191115, 01:33  #36  
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}×7×11^{2} Posts 
Quote:
How do you figure out a determinant? Edit: (I think) I at least understand what a Latin Square is. . . Last fiddled with by EdH on 20191115 at 01:34 

20191115, 03:32  #37 
"Rashid Naimi"
Oct 2015
Remote to Here/There
1,931 Posts 
That one just comes naturally for me, for square matrices of any size.
Code:
matdet(a) https://pari.math.ubordeaux.fr/dochtml/htmlstable/ What do I win? Last fiddled with by a1call on 20191115 at 03:32 
20191115, 03:51  #38 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}×7×11^{2} Posts 

20191115, 04:30  #39  
"Rashid Naimi"
Oct 2015
Remote to Here/There
1,931 Posts 
Quote:
https://youtu.be/w6m951XE7M0 

20191115, 14:07  #40 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}·7·11^{2} Posts 
OK, I learned how to pencil and paper the determinants of matrices, so maybe I'll play. I created a Latin Square with 556434705 and then made a nonLatin Square with 309945592. Does this sound like I'm in the ballpark of knowing enough to proceed?

20191115, 15:19  #41 
Oct 2017
97 Posts 
For comparison of computing times:
My actual code permutating some digits of a matrix  Latin or not, but saving the total number of digits in the matrix  needs 1 hour and 51 minutes for 10.216.206.000 determinants, when I use one thread. Using two threads: twice this number in the same time. Using four threads: Don’t know the time, but I‘ll check it. 
20191115, 15:39  #42 
"Hugo"
Jul 2019
Germany
31 Posts 
Well, 9x9 is normally not done with pencil and paper. But doable, blockwise. And when talking of the "structure" of a matrix, there are many things to consider. E.g. symmetry, blockstructure (think of a Sudoku), norms of rows and columns, correlations between rows, geometric interpretation as volume of an ndimensional polytope, dot products of row or column vectors. For Latin squares and their special cases of circulant or Sudoku matrices all 1 or 2norms of rows and column vectors are identical.

20191115, 15:47  #43  
"Ben"
Feb 2007
6342_{8} Posts 
Quote:
Since the recent pseudohints I've looked more at matrix structure but discovered nothing useful. I'm tending to either immediately rediscover det=929587995 circulant latin squares or find nothing but singular matrices... 

20191115, 15:57  #44 
"Ed Hall"
Dec 2009
Adirondack Mtns
2^{2}·7·11^{2} Posts 
I have set the paper and pencil aside now that I think I know a tiny amount of what I'm doing and started using machines to play. If this gets me sidetracked. . .

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