November 2019

[SmartMersenne]

Signing off

[yae9911]

Originally Posted by a1call

... there are no real shortcuts to the solutions,

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.

[EdH]

Originally Posted by a1call

Wow, that is sooooo discouraging. Assuming I am reading this right, not only has the open question been positively surpassed, but it has done so at least twice. While I have only inched forward still staying way below the threshold.
One comforting positive assumption is that since there are no real shortcuts to the solutions, the tiebreaker must be the computing power of the hardwares used rather than the that of people who use them. Or at least that's what I tell myself to keep from feeling like a total idiot.

Think how I feel:

How do you figure out a determinant?


Edit: (I think) I at least understand what a Latin Square is. . .

[a1call]

Originally Posted by EdH

Think how I feel:

How do you figure out a determinant?

That one just comes naturally for me, for square matrices of any size.

matdet(a)

https://pari.math.u-bordeaux.fr/dochtml/html-stable/

What do I win?

[EdH]

Originally Posted by a1call

. . .
What do I win?

My respect? in actuality, what I meant was kind of more of a definition that would allow me to understand what it is and how, in a long way to "pencil and paper" it. But, this is a start. Perhaps from here, I can find the other.

Thanks!

[a1call]

Originally Posted by yae9911

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 tell myself a lot of things:

https://youtu.be/w6m951XE7M0

[EdH]

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 non-Latin Square with 309945592. Does this sound like I'm in the ballpark of knowing enough to proceed?

[Dieter]

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.

[yae9911]

Well, 9x9 is normally not done with pencil and paper. But doable, block-wise. And when talking of the "structure" of a matrix, there are many things to consider. E.g. symmetry, block-structure (think of a Sudoku), norms of rows and columns, correlations between rows, geometric interpretation as volume of an n-dimensional polytope, dot products of row or column vectors. For Latin squares and their special cases of circulant or Sudoku matrices all 1- or 2-norms of rows and column vectors are identical.

[bsquared]

Originally Posted by Dieter

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.

Speed is similar here: 1 hour 25 minutes for the same number of determinants. I've learned a lot about determinants with this challenge, so all is not a waste. For example my first effort computed the determinant recursively, which is O(n!), I think. Anyway it was slow. Then I read more and (re)discovered Gram-Schmidt QR decomposition. That improved timing by a factor of 1000 or more. My current approach saves even more by remembering the Q-portion of the previous computation and only recomputes starting from the first modified row of the next matrix.

Since the recent pseudo-hints 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...

[EdH]

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. . .