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feos wrote:
- How do we define an ending?
Similarly to how we define it in other games: if the game has an ending, voila; and if it doesn't, we end on completion of last unique gameplay (or hardest loop, or highest score, or kill screen).
Are there even any board games that don't have an ending?
On the topic of chess variants, there are a good number with non-standard rules. This guy has a list. IDK of any video games that implement those (not that I've searched extensively), but it might be interesting to see some type of ACE setup that converts standard chess to one of the others.
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FractalFusion wrote:
We wish to maximize the area of the kite we construct. What is the value of x (the length of the dotted line in the diagram above) that gives the maximum area, and what is the maximum area?
I will be using the variables p and q as defined at MathWorld, so the desired area is A = 0.5 p q. In our case, p = sqrt(16 - 0.25 x2) + sqrt(49 - 0.25 x2) and q = x. To simplify some of the calculations, I'm using the additional variables e = sqrt(16 - 0.25 x2) and f = sqrt(49 - 0.25 x2).
The maximum value of the area occurs at a value of x at which the first derivative A'(x) = 0. Apply the product rule, chain rule, etc. to get A'(x) = 0.5 (e + f) [1 - x2/(4 e f)]. This means that either e + f = 0 or 1 - x2/(4 e f) = 0. There are no solutions to e + f = 0 among the real numbers. The other case can be rewritten as x2 = 4 e f. If you square both sides, expand the products in terms of x, and simplify, you get x = 56/sqrt(65) and A = 28.
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The elementals don't "come and go" as much as they orbit around Kuros's position. I made a Lua script some years ago that draws their movements. Anyway, nice improvement. Yes vote.
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adelikat wrote:
Yes, I wrote a program that pulls the values from the database and makes .wch files that I can upload, so I will do that
I previously reported incorrect Edit links for some of the addresses. Note that I did not check every single one, and IDK if the cause of that has been determined and fixed. Is there going to be some verification process to make sure that the pulled values actually match up with the correct games?
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That was a nice explanation. I tried to approach it by calculating the probabilities of sequences that require x moves starting from some number n. It was simple enough for x = 1 and x = n - 1, but other values of x got complicated. Ended up with harmonic numbers, sums of harmonic numbers, sums of products of differences of harmonic numbers, and who knows what happens after that.
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OmnipotentEntity wrote:
I haven't fully digested the content of your post. But I have worked a problem very similar to this with respect to neutron slowing down in my college courses. So I would expect them to have the same answer, which is log_2(N).
My mistake was in thinking that every sequence for a given N has the same probability of occurring as every other sequence for that N. I'll have to do some more work on this.
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FractalFusion wrote:
You start with a positive number N>1 and want to get down to 1 in a number of moves. Each move consists of going from the current number to a smaller positive number random based on uniform randomness. That is, from k, randomly go to a number 1, 2, ... , k-1 , each with equal probability. Keep doing this until you reach the number 1.
...
Starting from N, what is the expected number of moves to reach the number 1?
I initially did this by writing out possibilities and looking for patterns, so here's hoping that the following symbolic solution doesn't make any horrible mistakes:
Let M(x) be the number of sequences leading from x down to 1 via the method described in the problem, where x > 1. When the starting number is N, there are N-1 possibilities for the next number in the sequence. Call this next number k. If k = 1, then we're done. For each 1 < k < N, there are M(k) sequences leading from k down to 1 that we need to include in M(N). Thus M(N) = M(N - 1) + M(N - 2) + ... + M(2) + 1. That last 1 is for the N→1 case. However, M(N - 2) + ... + M(2) + 1 is just M(N - 1), so M(N) = 2 M(N - 1). Obviously, M(2) = 1, which leads to M(N) = 2N - 2. Since each move occurs with uniform randomness, the probability of any sequence occurring that starts with a given N is 1/M(N).
Now let m(x) be the total number of moves in all sequences starting with x. We can deal with the total number because each sequence occurs with the same probability. If a sequence starts with N→A and has n moves, then the subsequence starting with A must have n - 1 moves. There are M(A) such subsequences, so we add M(A) moves in order to adjust for the extra N→A move in each one. This leads to m(N) = 1 + ∑ A = 2N - 1 [m(A) + M(A)]. The extra 1 is for the N→1 case. If you write out the sum, you notice that m(N) = 2 m(N - 1) + M(N - 1). You can do this substitution repeatedly to get a more general m(N) = 2x m(N - x) + x M(N - 1). m(2) is 1, so it would be nice to take x = N - 2 in order to not have to worry about that m(N - x). This yields m(N) = N 2N - 3 after some work. Finally, the expected number of moves is m(N) / M(N) = N / 2.
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Requesting that the "minor edit" wording for wiki and forum changes be changed to something like "trigger Discord / IRC notification" and be unchecked by default. I believe that would clarify what that feature does.
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I agree with what scrimpeh wrote and think that the term should be kept as is. If it is changed, what do you think will keep people from becoming afraid of the new term?
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feos wrote:
CoolKirby wrote:
Also, if (almost) all submissions have a Game, should Userfiles as well?
Yes. And game resources too.
Is there a way to generate a list of Userfiles without an associated Game? I went back through my files in the last few days and made associations where possible, but some of them are general-purpose scripts.
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The submission notes are rather short. Why did you choose those specific criteria for a "perfect run" rather than other criteria? I have only watched the first 3-4 minutes but have already seen missed shots, a lot of hesitation in movement, and you going out of the way to get those little pink pellets that I do not remember being useful.
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OK, I finished watching the run. You obviously put a lot of work into it. I liked the glitches that you showed off and how you got 99 lives. However, I found it very repetitive even when watching it in small chunks over several days. By the fifth or tenth or twentieth time you
spawned objects out of thin air or
killed Yoshi only to immediate get Yoshi back or
changed terrain or
clipped through the ground or
glitched out the graphics or
backtracked within the same level or
backtracked on the map or
paused the game or
died (because of clipping into terrain?),
I was wondering what was so special about that specific event compared to all of the previous ones. Maybe the repetition would not have been as much of an issue in a shorter run, but this was nearly three hours, and it looked like there was more repetition than unique content. Consequently, I was not entertained and will have to vote No on this one.
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I learned about this via Discord: SNES Super Stars Marathon 2022 for SNES/SFC games. Submission deadline is May 2. Per messages in the marathon's Discord server, TASes are allowed.
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Since the Wiki: Games page literally says "Game groups by franchise," I can kind of see fan games and pirates fitting that idea despite them not being "official" releases in the franchise. I don't think that I would put 8 Eyes with Castlevania, though, since they had separate development teams, publishers, and commercial releases.
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p4wn3r wrote:
This week's Riddler classic is a pretty standard number theory problem. Find a six digit Carmichael number which can be written as ABCABC in base 10. As the Riddler notes, try to solve without writing a brute force code, you learn a lot of number theory doing this.
I kind of brute forced it, but not via code. Let n = ABCABC = ABC * 1001 = ABC * 7 * 11 * 13. This means that 6, 10, and 12 must divide n - 1. Take the prime factors of those numbers, and you get that 2, 3, and 5 must divide n - 1. Therefore, so must 2 * 3 * 5 = 30. So we have 30 x = n - 1 for some x, or 30 x + 1 = n.
Here's where the brute force comes in. Since n is odd, C must be one of 1, 3, 5, 7, 9. Let's assume that C = 1. Then we have 30 x + 1 = 7 * 11 * 13 * (10 * AB + 1). You can simplify that to 3 x = 7 * 11 * 13 * AB + 100. Taking everything modulo 3, you get 0 = 1 - (A + B). You can generate a list of the values of A and B that satisfy that relationship. It turns out that A = 1, B = 0, C = 1 yields a Carmichael number (I used this to confirm that 101101 is a Carmichael number) with the desired properties:
Its prime factors are 7, 11, 13, and 101, none of which is a square.
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scrimpeh wrote:
What was that final boss.
Certainly a contrast to the rest of the game. It was a last-minute addition, according to Mukunda Johnson.
scrimpeh wrote:
Anyway, coordinating the characters and routing out the levels seems quite involved
Yeah, I started over several times as I worked out the various mechanics, tricks, and glitches. Good thing level 6 is the only one that has synch problems.
ThunderAxe31 wrote:
You mean "final" until now, right?... right?
Honestly, there aren't many games that interest me, don't have runs already, and run on one of the site's preferred emulators that I can use.
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There does not appear to be a way to add new games to the Wiki: Addresses-List page. Either that, or I don't have the proper permissions. But I can still edit Wiki: GameResources. Furthermore, the Edit links for the address lists seem to be messed up. Some examples:
Trying to edit A2600 Barnstorming leads to a page that says Genesis Chiki Chiki Boys
Trying to edit A2600 Bobby is Going Home leads to a 404
Trying to edit GBC Bionic Commando: Elite Forces leads to a 404
Trying to edit NES Wizards & Warriors III: Kuros: Visions of Power leads to a page that says NES Super Mario Bros. 2