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I didn't find Tricky Maneuver very difficult, but I don't think I used the intended path either. Hopping right off the checkpoint block and then taking a hard left, you can get to the lower-right crumbling platform without using the gravity line or the platform underneath the start at all. Maybe that's unintended.

I gave up towards the end of Zone 3 though. I forget the name of the room, but there's a difficult spiky path off to the left (which is longer than it needs to be, I think) and a warp off to the right which leads to a room with gravity lines that I can't figure out.

EDIT: Oh, I see. It used to be harder.

Yeah. VVVVVV without flags may very well be in NP!

You're totally right! Here's a proof, assuming fixed room size.

For a particular set of crewmates rescued and trinkets collected, the current "status" of a player in a flagless VVVVVV game is determined by the following choices:

-Position (choices bounded by a linear function in the number of rooms).

-Velocity (bounded by a constant).

-Current gravity direction (2 choices).

-Location of most recent checkpoint (bounded by a linear function in the number of rooms).

-Current status of crumbling platforms in current room (bounded by a very large constant).

-Current location and velocity of enemies in current room (bounded by an even larger constant).

-Current location and velocity of moving platforms in current room (same).

-Whether each scriptbox or terminal in the current room has been activated (bounded by an even larger constant).

-Whether grav lines, warp tokens, or platforms have been destroy()ed yet in the current room (8 choices).

And that's it, unless I'm forgetting something. So if we represent each combination of these choices as a vertex in a directed graph, and draw an edge from u to v if it's possible to get from state u to v in one tick of the game's clock (by some combination of pressing left, right, and/or action), then we've got a directed graph on a number of vertices that's quadratic in the number of rooms.

Some of those vertices (based on the position of Viridian) correspond to acquiring trinkets and some correspond to rescuing crewmen, and a solution involves picking those up in some particular sequence. But again, the number of trinkets (even ignoring the current cap at 20) and the number of crewmen (is there a cap? Even so....) is bounded by a linear function in the number of rooms.

So the total time to get from one position to the next trinket/crewman is O(n^2) since it's at most the diameter of the graph, and the total number of crewmates and trinkets is O(n), so the time to finish the level is O(n^3). Now granted, the cubic in question has a leading coefficient that's larger than the number of atoms in the universe, but a cubic is a cubic. So yay!

(Note: all of this falls apart if you let room sizes increase, like in The Tower but without the forced scrolling. I've almost succeeded in making a Towers of Hanoi puzzle using breaking platforms and moving enemies, to the point where I think a more clever designer could pull it off. Make a tall enough room and BAM! 2^n solving time.)

If I understood half of that... I might actually play it. But WHAT THE HELL ARE YOU EVEN TALKING ABOUT?!

Heh. No worries, you're only 14. But if you want to look up some of the terms you don't know on Wikipedia, I bet you'd find it enlightening and not that hard to understand. I learned most of this stuff when I was 16, and you seem like a reasonably smart kid, so it's worth a shot.

Awesome, awesome work. Always nice to learn something new. Nice to see such passion for this game. Great level design, too. Just one flaw - the crewmates can be skipped. I suggest you use gravlines to block the exit wires, and place a [flag(X, on) destroy(gravitylines)] script on top of the crewmate, and [ifflag(X, [destroy(gravitylines)]] on the entrances. That way you only have to beat the challenge once.

Yeah, I thought about that. But as far as the proof is concerned there's no problem with crewmates getting skipped. The point is that a solution exists if and only if the formula can be satisfied, not that a solution is inevitable. So we only need to "idiot-proof" the level enough that an incorrect player can't win. It's fine if a correct player can lose, as long as it's because of other decisions he made. I decided to leave it this way, just so that the level itself could be constructed without scripts. (Well, besides the music ones.)

Vex69, you're a speed demon! I have no idea how you downloaded the level and read enough of the text to beat it and comment within 15 minutes of my post, but I'm super impressed.

I can't see the practical use of the result, but it was a fun read.

I'm a pure mathematician. Please don't use the p-word around me.

Of course, this only works for generalized VVVVVV, that is, without the 20x20 size constraint.

Yup. Likewise, for the exercise I mentioned in the top-right terminal of the second room, you need to allow arbitrarily many flags rather than capping at 100. (At least in the solution I'm thinking of.)

http://www.destructoid.com/blogs/knutaf/a-mathematical-and-inquisitive-approach-to-vvvvvv-184093.phtml

Ha! Nice. I'm not sure I can parse the conditions in the theorem in a way that doesn't make it (a) trivial or (b) false, but the approach is pretty great.

[CHANGELOG:]

My first level! It's... pretty different from all the other levels on here, at least.

As the title suggests, the level walks through a proof that determining the solvability of a VVVVVV level is NP-hard. (Spoiler: we reduce to 3-SAT.) After some (very) lengthy exposition, an example is given to demonstrate how a particular instance of 3-SAT would be represented and solved.

The layout loosely resembles an academic paper. If you don't know anything about complexity theory then this whole thing probably won't make any sense at all, but if you have a passing familiarity with NP-completeness then I think you should be able to follow what I did here.

It's a 5x5 level, and every room is used. Difficulty-wise there are almost no dexterity challenges, but if you're unfamiliar with Boolean logic then you might find it confusing anyway.

Hope you all enjoy it!





CHANGELOG:

Version 1.0 (Released Oct. 1, 2011)
-Initial release.

Figured it out: don't end a line of dialogue with a colon, or the program will think it's a new script.

I've had some weird issues with script lines disappearing. Most often I'll finish a script, then when I reopen it again the last line is missing. Most recently I wrote a twenty-something-line script, then reopened it to find that only the first three lines were there.

Is this a known bug? It seems like something that would come up for more people given how often I'm seeing it. Any way around it? So far my technique is "just write the lines again", but that doesn't actually work a lot of the time.

Cool concept, but I agree that the difficulty drop wasn't quite as noticeable as you were going for. Hairpin was by far the hardest level for me (racked up about 200 deaths there), while ↑ and Down was pretty easy. Boo! Think Faster! Was probably the second hardest (which is good, since it was the second room), so I'd swap Hairpin with the first.

If you really want the difficulty to decay exponentially, then the most noticeable difference should be between the first room and the second. I think putting Hairpin there would accomplish that pretty well.

Also: super mean with the warp lines on the third floor! If you're not careful it's easy to send yourself back two rooms at once with a little careless exploration.

Haven't finished yet, but I'm really liking it so far. I laughed out loud at the "Delta Blues" pun. One quibble: the comma in "Wherefore Art Thou, Romeo" makes absolutely no sense.

I absolutely loved most of the level, but the ending was super mean. If you have the warp token on the left side of the screen like that, people like me are gonna jump into it right away just to see what it does. So much of this level's design is about taking leaps of faith and sometimes (okay, okay: often) ending up with a grizzly death, but that only works because the game won't send you back very far when you're unlucky. To subvert that at the very end and require players to start over? Not cool man.

Awesome challenges throughout (I'm one of the people who did the compactor puzzle the hard way), but it was sad not to be able to finish it.

Quick question: in the level editor, it seems that breakable platforms don't block moving ones as they do in Laboratory 2 (Prize for the Reckless, Exhaust Chute). Any particular reason for that?

Some really clever and tricky bits here. I'm completely stuck trying to get into the treasury, though. Is there a good way to get past the rightmost part side of the screen above it, with the vertical bounce lines?

Today I wondered what would happen if, during the Space Station 2 time trial, I went north from Exhaust Chute and hit a checkpoint at Drilling Down. Would I be stuck?

Naturally, Terry thought of this and put invisible spikes on the ceiling of Exhaust Chute for the time trial, but I was a little disappointed by that workaround. Could we maybe get something slightly more clever, like a horizontal bouncer near the ceiling (but below the checkpoints) of Drilling Down? Something more than instant death to reward players for their curiosity, y'know?

Sure, but how do you get it in No Death mode? 

Finally figured out the answer to this question while playing time trial. Heh.

You can always come back and try later; sometimes hard challenges like this get more difficult as frustration starts to set in; you can't react as quickly when you've been attempting the same thing for hours.  I bet if you play around with other VVVVVV things for a bit, DTTHW will be significantly easier when you return.

Definitely. My first run through DTTHW took around 200 deaths, but the screenshot I posted a little while ago was done in under 20. Vici-Vidi-Veni on the way down is a piece of cake, after you've done it once.

Not really a "review" per se, but I wrote a little post about it and another game here: http://thegutterblog.wordpress.com/2010/01/12/hoggy-vs-vvvvvv/