Al Zimmerman - Delacorte Numbers

[whitefox]

Pavlovsky
Ваш вывод проще моего.

Я же использовал формулу:

whitefox в сообщении #930921 писал(а):

$$D_k=\left(\left\lfloor\frac{n^2}k\right\rfloor\sum\limits_{i\in M_k}\left(x^2_i+y^2_i\right)\right)-\left(\left(\sum\limits_{i\in M_k}x_i\right)^2+\left(\sum\limits_{i\in M_k}y_i\right)^2\right)$$

для $k=1$ и расположении начала координат в центре квадрата.

При этом рассматривал отдельно случай чётного и нечётного $n.$

[jcmeyrignac]

yae9911 в сообщении #951655 писал(а):

Or try to find Max12. The corresponding record seems to be held by not too many participants.

How can you say that ?
Do you know what the top for Max12 is ?
Do you know what other participants achieved ?
I'm very curious about your Max12, could you share a lower bound ?

It's obvious that if you want to be in the top 10, the easiest points can be achieved in Max<=13 and Min<=15, because larger grids require a lot of time to just save a few hundredths of point.
My partner and myself spent a lot of time on small grids, and we are not even sure if our Max9 is optimal.

[yae9911]

jcmeyrignac в сообщении #952136 писал(а):

yae9911 в сообщении #951655 писал(а):

Or try to find Max12. The corresponding record seems to be held by not too many participants.

How can you say that ?

I've found the current record on Dec 3rd and submitted it a few days later. Since all competitors dropped, I'm sure my result was TOP(Max12) at the time of its submission.

JCM писал(а):

Do you know what the top for Max12 is ?

If mine still holds, yes.

JCM писал(а):

Do you know what other participants achieved ?

No, but most likely not significantly better, because otherwise it would have had a greater effect in the standings.

JCM писал(а):

I'm very curious about your Max12, could you share a lower bound ?

Not at the moment

JCM писал(а):

It's obvious that if you want to be in the top 10, the easiest points can be achieved in Max<=13 and Min<=15, because larger grids require a lot of time to just save a few hundredths of point.
My partner and myself spent a lot of time on small grids, and we are not even sure if our Max9 is optimal.

None of the results for N<=11 has moved since a long time, at least not until Arch D. Robison's attack.

[jcmeyrignac]

yae9911 в сообщении #952207 писал(а):

None of the results for N<=11 has moved since a long time, at least not until Arch D. Robison's attack.

Oh, I didn't recognize you Hugo.

You have to remember that we started to submit our grids when the score had two decimals, and at the time we got a score of +1 for every submission (as long as you had more than 0.995, it got rounded to 1 point).
So now, we have no idea if our grids are good or not.

This is really the most annoying part of Al's contest: when you submit early, you lose a lot of information.
The best strategy is always to submit when the scores became stable enough.

[yae9911]

jcmeyrignac в сообщении #952501 писал(а):

yae9911 в сообщении #952207 писал(а):

None of the results for N<=11 has moved since a long time, at least not until Arch D. Robison's attack.

Oh, I didn't recognize you Hugo.

Since any search engine will inevitably decode my user name, the attempt to hide was rather weak

jcmeyrignac писал(а):

You have to remember that we started to submit our grids when the score had two decimals, and at the time we got a score of +1 for every submission (as long as you had more than 0.995, it got rounded to 1 point).
So now, we have no idea if our grids are good or not.

For the Max problems we have used the relative position of results against the theoretical maximum as described previously by Pavlovsky. Hermann had already independently derived this bound before. If one fits a smooth function to the difference of the own current results against the upper bound, then it's easy to see where to use the available computer ressources, at least for N>=19. For smaller N the scatter is too large to use it as an indication of quality. For the Min problems so far no similar bound seems to be known?

jcmeyrignac писал(а):

This is really the most annoying part of Al's contest: when you submit early, you lose a lot of information.
The best strategy is always to submit when the scores became stable enough.

Well, you know from good old times when we jointly organized previous contests, how much fun it was fighting for the TOP flags. But it's Al's contest, and we have learned to arrange ourselves with his opinions.

[dimkadimon]

yae9911 в сообщении #952549 писал(а):

Well, you know from good old times when we jointly organized previous contests, how much fun it was fighting for the TOP flags.

I miss fighting for the tops too. I have no chance of winning, but at least I can get a top. So it really gives me a sense of accomplishment. Al seems to be worried that people will hold on to their results until the end and it will make the competition boring, so he doesn't reveal when tops are reached. However, I have never seen this happen in any competition that I've done.

[jcmeyrignac]

yae9911 в сообщении #952549 писал(а):

For the Min problems so far no similar bound seems to be known?

I'll give you the one I use, which has been deduced from our results:

$$f(n)*\frac{n^4(n^2-1)}6$$

where f(n) varies smoothly from 1.1 at n=3 to 1.7 at n=27.

[yae9911]

@whitefox: Have you started submitting to AZ's contest website?

[whitefox]

yae9911 в сообщении #953408 писал(а):

Have you started submitting to AZ's contest website?

Нет, я этого не делаю. И не спрашивайте -- почему? Сам не знаю

[Pavlovsky]

Война рекордов продолжается. Лидеры потеряли элитные 24.999.

Цитата:

1 24.998876 Tomas Rokicki
2 24.998830 Arch D. Robison

[dimkadimon]

Mожет поэтому:

Цитата:

228 15.00000 Hermann Jurksch & Hugo Pfoertner Recklinghausen & Munich, Germany 31 Dec 2014 02:05

[jcmeyrignac]

dimkadimon в сообщении #954714 писал(а):

Mожет поэтому:

Цитата:

228 15.00000 Hermann Jurksch & Hugo Pfoertner Recklinghausen & Munich, Germany 31 Dec 2014 02:05

Al removed one digit in the scores, so this just means that H&H have a score > 14.999995

[dimkadimon]

Who will win?

Цитата:

1 24.99986 Hermann Jurksch & Hugo Pfoertner Recklinghausen & Munich, Germany 1 Jan 2015 11:00

Цитата:

205 22.99995 Anton Nikonov Noginsk, Russia 31 Dec 2014 22:22

[yae9911]

dimkadimon в сообщении #954993 писал(а):

Who will win?

Цитата:

1 24.99986 Hermann Jurksch & Hugo Pfoertner Recklinghausen & Munich, Germany 1 Jan 2015 11:00

Цитата:

205 22.99995 Anton Nikonov Noginsk, Russia 31 Dec 2014 22:22

It depends on remaining fuel. If Anton can go two miles, he could win the contest. Otherwise he might win a bet ...

[Herbert Kociemba]

dimkadimon в сообщении #952933 писал(а):

Al seems to be worried that people will hold on to their results until the end and it will make the competition boring, so he doesn't reveal when tops are reached. However, I have never seen this happen in any competition that I've done.

I have a different impression in this contest.