November 2019

[yae9911]

Originally Posted by Dieter

Now I have found a matrix which is no Latin Matrix (same digits in the same line) and has a determinant 924844032, and each digit appears 9 times.

If there is a Latin Matrix with the same determinant - I don‘t know.

Guess why I mentioned OEIS. A309259 excludes both of your reported determinant values being determinants of a Latin square.

[yae9911]

Originally Posted by axn

I believe you (general you) are misinterpreting the puzzle. Sure, the plain wording does suggest that particular interpretation. But I believe the intent is to just avoid latin squares, period, and not determinant values arising from latin squares. Perhaps asking for a clarification is in order?

The motivation to use this wording was to inhibit that someone finds a non-Latin square with exactly the already shown value of the maximum Latin-square determinant. Nobody could give me an answer of the question "is it possible to construct a non-Latin square with determinant 929587995"?. All possible determinant values of 9x9 Latin squares are known from an (yet unpublished) enumeration expanding the data given by Brendan McKay. I can provide more information after the end of the submission period. If you should find a Latin square with determinant in the range [loophole barrier, record] I'm extremely curious to see ist.

[LaurV]

Looks like you know exactly what you are talking about
From which we could assume that you are Mr. Pförtner? (the OEIS sequences with your name attached to them are quite fresh, and I assume this is a very actual domain of your interest, and I see you are also the one who proposed the puzzle - this is indeed an interesting puzzle)

[bsquared]

Originally Posted by Dieter

Update: 928284672
Unfortunately my code has a bug, which I try to find, but I have checked my results externally before presenting them here and sending them to the puzzlemaster.

That is quite impressive!

Largest for me is now 925119207 but I have no other ideas for how to find larger values. I'm just throwing CPUs at it now.

[yae9911]

Originally Posted by LaurV

Looks like you know exactly what you are talking about
From which we could assume that you are Mr. Pförtner? (the OEIS sequences with your name attached to them are quite fresh, and I assume this is a very actual domain of your interest, and I see you are also the one who proposed the puzzle - this is indeed an interesting puzzle)

It is probably hopeless to deny that I am that person. Years ago, we wrote an article about upper bounds of determinants, and in the update to this by Markus Sigg, just the non-Latin determinants using the multiset [1^n,...,n^n] come as an example. Actually, the topic would have been done, but by coincidence, I recently came across the OEIS files of the students research group, who have just dealt exactly with the determinants of Latin squares. It was logical then to look at their relationship with our bound. n = 9 was just the first open problem, and now we are on the subject. Same question as in the puzzle also for n=10, ... if you have abundance in unused computer resources. Much more promising would be good ideas regarding a structure of the matrices.

[SmartMersenne]

Originally Posted by bsquared

That is quite impressive!

Largest for me is now 925119207 but I have no other ideas for how to find larger values. I'm just throwing CPUs at it now.

Yes, both are!

[Dieter]

I‘m very embarrassed, but my two results are wrong. The determinants are not correct. I knew that my code had a bug (meanwhile corrected), but I‘m astonished that the online calculator I have used for control yields the same wrong results.

[Kebbaj]

I sit on the ground and I look at this: 930 174 030.

[SmartMersenne]

Originally Posted by Kebbaj

I sit on the ground and I look at this: 930 174 030.

Do you mean this is the highest you found?

[yae9911]

Originally Posted by Kebbaj

I sit on the ground and I look at this: 930 174 030.

Will earn **but not *

[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.