Saturday, 26 November 2022

AD4 and more in Windows 11

Just as the time we turned into Windows 10, Windows 8, Windows 7 or beyond...it's time for us to solve compatibility issues.

From 10 to 11, they changed more on UI but we were not driven too far away from the old system: many of the changes made in system settings and control panel were already in later updates in win10. They removed some more personalization utilizes since then, but you can pretty much do everything as in the previous versions.

One big complaint though, is how they removed the shortcut keys in the file explorer, like W on right click to create new folder...why must I move my cursors there? Even more interesting, the Win10 file explorer is clearly intact -- for example when you choose the save destination in browsers you get the original file explorer as in Win10. I however tried to apply registry changes to block the new Win11 from loading forcing the old one but no luck, I guess they blocked these naive methods...

Desktop only input method

Since the introduction of MetroUI, it has been a problem to use those old input methods as they do not fit with MetroUI. They changed quite a lot in language settings, giving more of a hard time for these input methods.

I installed the old input method just fine in Windows 10, but in order to activate the Ctrl-Shift shortcut to change the input methods, one needs to install multiple language and multiple input methods to those languages. For example it won't work if you only have Chinese language installed with "Microsoft default input method + some old obsolete input method". Instead you install the Japanese package as well then it works with "Microsoft default input method + some old obsolete input method + Japanese input method". (For more: IME disabled in Windows 11/10)

In Windows 11 I have to apply a registry change in order to get the input method going. These fixes are nothing new but once you have to do that you know what you have been using is another step into the swirl of compatibility issues.

After Dark 4 and screensaver

The screensaver function were kept largely the same in Win11. At this point we can pretty much set everything via registry that changes in the setting menu don't matter anymore unless they completely removed screensaver...

What I wrote about installing AD4 in Windows 7 and 10 still works in Win11. Install in WinXP compatibility mode, retry if a file can't be installed and skip if a file was missing. Use the .bat file from the YouTube video to apply settings to those AD screensavers. I actually spent less time installing it in Win11 than on 7 and 10!

Thursday, 17 November 2022

Simon Marais 2022

So this year I am not almost a year late. It's always a joy for me to deal with these questions. Here are my immediate thoughts after reading the scripts -- immediate means that I didn't put any serious effort into it and didn't do any calculations that requires pens and papers.

One changes they made was to split the tournament into two time zones to reduce the chance of possible cheating but I can only say that it's far to easy to cheat at institutional level if they wanted to...but the good news is that we will get four more questions to solve.

A2. A very nice combinatorial little question but should be A1 in my eyes. The $e^{-2}$ made me think of derangement since $n!/!n \approx e$ but no luck in that. Eventually you realize that the question is much much easier -- this is just the chance of an item appearing in at least one but not all $n$ subsets, for all $2^n$ elements.

A3. IVT because why not? But I don't like this question due to the lack of elegance...

A4. Two parts in the question. Showing that to be an integer is a standard high school MO question. The second part...something with field if it's put as a Q4? Bad luck if you didn't do enough math olympiad in high school.

B2. Question that I love so much because imagine getting that in the 1985 A-level (HKALE) pure maths paper! This is not a joke and is totally possible. Since the non-zero terms are of even degree, the roots are symmetrical along the real axis, hence the circle centre is real. That means the roots are on a circle centered at origin upon a real translation. Boom!

B3. Easy if you consider the "1D" version first. This game can't be any simpler...

B4. (a) is easy as a Q4a (unless I made a mistake): classify $2[b_n/20]-3[a_n/30]$ based on $a_n-b_n$ in intervals of 10. Since the difference between that term and $(b_n-a_n)/10$ is at most 3 that gives you the idea of splitting the cases $a_n-b_n$ being either between -10 and 20, above 20 or below -10. The first case gives the induction and the latter cases gives strict monotonicity which gives the claim. 

(b) is surprisingly elegant as an open question. It is not easy to think of other open problems as simple as this other than the 3n+1 conjecture.

C2. ...why? Instead of a A-level pure maths question you give a calculus I assignment question... The ceiling function means that ceil(sin x) is either 0 or 1. The irrationality of $\pi$ means that the term is negative, hence rounded up to 0, at least $0.5 - \varepsilon$ of the time. If irrationality is too hard, it is still easy to argue that at least one out of four consecutive terms is of power -1 (diverges) instead of -2 (converges), then the comparison with $\sum \frac{1}{4n}$ gives the desired result.

C3. Classic MO question again. If you are not sure, consult lower cases like $n = 7, 12, 17...$ etc.

C4. Another good question but looks quite intimating other than the $(n-1)!$ term who's there for the obvious reason.

You ask me why aren't there Q1s above? The answer is clear: they do not worth talking at all. Q2s are very easy (probably of Q1 level in past papers or even lower) in my eyes but Q1 are even easier. They looked ugly and tedious, but not hard. Q3s are easy to moderate, but I don't think they are as hard as Q3s in the past. Q4s are hard as they should be, but that means the Q3-Q4 gap is even larger. 

This is not a very good contest paper not just in terms of difficulty spread, but also in terms of the scope -- many of the questions are plain high school MO level. Take 2021 putnam for example and check what they used: non-integral binomial theorem, qZ rings, double integrals, fancy polynomial about primality, geometric probability, infinite sum, Green's theorem (if you don't recognize B3), matrices and determinants. These are things that contestants are expected to use inside that examination. They should really expand in terms of number of questions with more challenging ones (but not as hard as those Q4s) and make sure that college maths were cooperated into the questions...

Sunday, 13 November 2022

Thoughts on CTWC2022 final

Best moment of CTWC22': (1) The unimaginable 2mil+ score and (2) 80k lead is like nothing... Source

This is the first live event held in reality since covid in 2020. Everything was done in 3 days so you don't get the week by week excitement so it's kind of a different experience. I only watched the final feed when they uploaded that today though, so here is my thought.

When aGameScout talked about top 6 players around, it's quite clear that the top 4 players as top 4 seeds are better than the rest. Among the four the top 2, Eric and fractal are also above the other two by a significant amount. It is almost expected that they would meet in the grand final.

I thought they put the lv49 level cap in effect but apparently they don't, and it's nice that they didn't cause otherwise we won't have the wonderful match extended to level 70 and beyond. The tactic of the two is clear: Eric relies on his consistency throughout and Fractal tried to be aggressive early on (which is why he made the record of Tetris streak in the semifinal). That would give him an advantage of 100-150k before level 29. This seems to be quite a lot in early post-29 levels but early reversible at very late stages (lv 50 and beyond) even with single and doubles. With that Eric withstood the headwind, patiently waited for Fractal's mistake and eventually caught up and took the 3 victories he needed.

The performance of the two had been very close from start to end. They performed almost the same not only in terms of score and efficiency. It may not be clear during online events, but when they share the same piece sequence it became apparent that they would meet difficulty at the same time other than a few scattered individual mistakes. That is true even when the two board looked different. Number of samples may not be enough but to me this is the result of a similar placement logic that it's just weak to similar piece sequence. That was mentioned in the last entry and now partially verified, although we won't have more live events in a short period time for now.

Like the past two years my roadmaps had been beaten over and over, but I shall not stop making predictions. For games like this it is always the trade between efficiency and consistency. There is a trade between the two, but there is no stopping you from improving yourself to raise the possible sum of the two. 

Last year when the rolling technique was still immature there were inconsistencies at even level 18 speed. But this year not only that they solved the problem, they even have excess consistency that can be converted into extreme efficiency at the same speed as demonstrated by Fractal. This is possibly a shock to other participants because if you are 100k or more behind it will be extremely hard for you to hold and catch up (lest you are Eric). This will probably become the meta in foreseeable months. It may not be as extreme as Fractal's strategy but there is a marginal return for consistency so it does not hurt to be a bit more aggressive when you are so proficient. 

Top rollers can deal with level 19 speed considerably steady as seen in the tournament. Fractal's aggressiveness does not apply here -- he try to be a bit more aggressive at game 4, took the pill, didn't work out and lost the game. In terms of input density it's more or less the same across strategies, but it's all about mindset and muscle memory. At level 18 speed top players are very relaxing and can very easily spare their time react to commentators or lifting their glasses. This is much harder at level 19 where they start to focus a bit more into the game. Decisions are made with instincts at this point so everyone is using a balanced strategy just like what they did in the past, including times when rolling wasn't a thing. Perhaps there will be players trying to play level 19 just like under level 18 speed, but this is not happening now.

And for post level 29 gameplay? Survival. You may be able to get Tetrises occasionally but there is nothing you can do if you topped out even if you lead by 200k points. It's just a matter of maybe 50 lines or even less, and as long as the opponent survives they will eventually overcome the deficit and takes the victory. 

Well, another possibility is if players managed to score triples and Tetrises much more frequently than they do now so that efficiency overwhelms survivability, but that would raise the average stack height by a lot more making that very risky for now. But who knows?

The grand final match was around 58 minutes long, a lot longer than the last year's average at about 38 minutes. Even with the excitement of level 29 gameplays that just too long. There had been voices to apply measures to shorten the games. Funnily, level 18 and 19 actually distinguished themselves in this year's final where level 18 is where you may take things to the extreme while you can't in level 19. I would take 'starting from level 19' as a solution in the past, but probably not now. How about shortening both level 18 and 19, say cutting 30 lines each? Admittedly they did not have the level 49 cap in effect which means that they are still playing the authentic game in full, but any further changes to the rules would likely deviate from the original game that we should not worry too much about that.

Some said that it is still far too early to talk about fatigue and the end of the techniques. Yes that is true. Players still evolved hugely this year and we still have considerable room for improvements. But the end is not that far away. Taking the learning curve of players into consideration I won't be surprised if anything I randomly baselessly claimed above actually happen in 2023/2024 CTWC or earlier. It would be the time for organizers to very seriously rethink about the tournament format. Some experimental changes may also be tested in smaller or online events as well. Just make some preparation before changes must be made.

At the end there is one thing for sure though. I enjoyed the tournament this year a lot just as usual, and I anticipate the one next year too. If you have no experience in classic Tetris you should really have a look at the clips and admire how people adopt and play games to the extreme. ;)