Do you have a map of the glowball stage?

Yeah, I think so. I can add it, but I didn't think it was particularly necessary.

May someone please tell me what the 'B' means and why that's on the gumball?

I believe the B stands for "Bubble".

I think the "B" means barrier, since all three shields have that B on them, and the shields do act as barriers to certain hazards

It's possible to get a ring bubble worth 30 rings. I don't know yet about other values.

A couple of observations:
1. In slot machine stage, you don't get the Continue if you hit the 50th ring inside the slot machine. You have to touch one of the rings outside. You can, of course, accumuate rings in the slot machine, and when you have a sufficient amount, touch an outside ring for the goodie.
2. In glowball stage, early ring bubbles can contain only 5 rings. Also, it's worth noticing that, if the vortex is getting close to you, you hear an alarm sound warning you to climb up fast.

Did you know theres a hidden 8th special stage that can be acessed by debug level select.

Yeah there is but I'm a little rusty on getting there, it would be helpful of you could include it here later.

Special Stage 6 only has 144 rings, not 160.

Planet 6 is more of a easy level and/or break from Planet 4 and 5.

Hey LiQuidShade, don't you think planet 7 is the hardest? It was my least favourite as a kid and I had lots of trouble with it.

I actually think Special Stage 4 is the hardest of the bunch, yet its so simple! The problem is you have almost no margin for error and if you jump too early over a sphere, you don't realize it until you reach the end when 1 sphere is unaccounted for. What a tease, >:o

There's a minor error in the map of planet 2. Heading north from the start position, the second 3x3 grid of spheres you encounter has red spheres at southwest, south, southeast, and center, when it should have them at west, southwest, south, southeast, and east - thus allowing you to get the spheres at northwest, north, and northeast and turn the grid into rings.

My least fave? tie between level 4 and 7. HATE HATE HATE HATE HATE HATE HATE both of them. The two things preventing me from being hyper sonic (without cheating) are thos 2 damn levels

ShadowXRouge 4ever!

It was difficult, but I managed to get a perfect in all these special stages, without save states. Yes, even stage 4, which was easier said than done. Getting perfects is easier in the Sonic 3 special stages.

Hyper Sonic. The ultimate game breaker. :) My favorite is always the Flying Battery main boss. In the first section, if you time the double jump right, you can go right through the barrier and onto the other side. You are greeted by glitchy clouds until the first part of the boss is complete

Annoyingly, if you have over 50 rings with Tails or Knuckles, you try to fly, or glide, and it turns you into Super/Hyper form, even with a shield. I'm not saying that Super/Hyper forms aren't cool, but sometimes we have over 50 rings and maybe don't wanna transform?

The color issues in KinS2 are caused by that darn red of Knuckles. :) The hacks that get him into Sonic 1 have the same issues.

134,217,728 is 2 to the 27th power.

Here's the deal with Blue Sphere.

Of course, they didn't design over a hundred million levels from scratch. Each Blue Sphere level is 32x32, so they designed a more manageable number of 16x16 quadrant tiles (128 of them) which are all modular; specifically, the left edge of the 4th row and the bottom edge of the 13th column are always open to guarantee a path will be available between the quadrants, and the starting point will be at one of these connections. Also, each tile is guaranteed to have at least 1 blue sphere and 1 ring so that obvious degenerate levels won't appear (though there are definitely some easy ones out there).

For simplicity, I'll label the quadrant you look upon at the beginning as Tile A. From A, turning left for 14 gridpoints (or, if the layout permits, turning right for 4 gridpoints) will put you in the next quadrant, "Tile B", which draws from the same pool of tiles, except reflected across the Y axis. If you turn around instead of going forward at the start, you'll be looking upon "Tile C", which is reflected across the X axis, and from there going 14 gridpoints right or 4 gridpoints left will put you in "Tile D", which is reflected on both axes (or rotated 180 degrees, if that's easier to visualize).

To get to the reason why there are two different numbering schemes for the levels, let's start with an explanation of the "stage" numbers, as opposed to the "level" numbers. With 128 tile layouts in the pool, and four spots to place tiles, the number of distinct levels you can create is 128^4 = 2^28 = 268,435,456 (note that this number is twice as large as the cited number of levels). In fact, a stage number is created simply by concatenating the 7-bit tile IDs chosen for A, B, C, and D in that order, and reading them back as a single 28-bit binary number. This is a rather straightforward operation for the machine to perform, but the stage numbers are held back in relative obscurity because they make for a terrible way of advancing through the game.

Observe what happens with the first few stage numbers: stage 0 = 0-0-0-0, 1 = 0-0-0-1, 2 = 0-0-0-2... The stages would be extremely repetitive to play that way, with each stage containing at least three copies of tile 0 until you get to stage 129 (0-0-1-1). Heck, in order to get the tile in front of you at the start to change from tile #0, you'd have to get over 2 million stages deep! Even with perfects all the time, that's far longer than anyone would reaonably put into the game, especially when each stage advancement changes so little of the layout for next time. (On the plus side, you'd at least have a lot of practice on your lines for getting all the rings in each tile.)

Their solution to that problem was to introduce the second, more visible metric--the level number--to serve almost like a hashing function, with the goal of mixing up which tiles appear when you advance from one level to the next. The algorithm to make it work is relatively simple, but it works like a charm. For level number N:
-Tile A is chosen as (N - 1) % 128. (% is the mod operator, which essentially asks you to perform long division but consider only the remainder, instead of the quotient. 13 mod 3 is 1, 256 mod 128 is 0, and 99,987 mod 10 is 7.)
-Tile B is chosen as (3N - 2) % 127.
-Tile C is chosen as (5N - 3) % 126.
-Tile D is chosen as (7N - 4) % 125.

Simply by making sure each tile ID increases by a different amount (and at least one) at every new level, and staggering the looparound points so they don't get into a pattern of going back to 0 all at the same time, they achieved their goals of making most successive levels feel sufficiently different, and having a numbering scheme that goes without repeats for a very long time.

It doesn't quite hit the full span of 268M+ stages, but the level scheme manages to stave off repeats until level 128,016,001. There are two factors responsible for this:
-Any number mod-125 will give a result from 0 to 124. As such, it's impossible for tile #125 to show up in position D. Likewise, tile #126 can't show up in C or D, and #127 can't show up anywhere except A. This causes a modest number of stages (okay, over 12 million of them) to be impossible to generate as a level.
-Observe the algorithms for tiles A and C. The number for tile A goes up by 1 with each new level, except in case of a rollover in which case it goes down by 127. Tile C goes up by 5 each time, or (at a rollover) down by 121. These changes are all odd numbers (unlike B and D, which decrease by an even number during their rollovers). For any given level, the numbers in slots A and C will either both be even, or both be odd. It's impossible to mix up their parities, so any stage number that has an odd A and even C (or vice versa) will never be visited by the level algorithm. This cuts the level space in half compared to the stage space, but it still leaves more levels than you could ever play in a lifetime, so suffice it to say that no one's complaining.

As far as difficulty ratings, each tile has its own hard-coded rating from 0 to 3. Determining the "difficulty" of a level is just a matter of taking the sum of all four pieces' difficulty ratings, then adding 1. Of course you may have your own ideas about difficulty that don't match what they programmed in. Heck, one of the tiles claims the peak difficulty of 3 while sporting 168 blue spheres, four rings (plus 160 more that can be converted from a giant square of blues), and no reds whatsoever! The code 3253-1444-7528 will give you a level with four copies of that tile, and probably the easiest difficulty-13 (MAX) level of the entire lot...assuming you don't fall asleep from all the sphere- and ring-collecting first.

A note about the Super Emeralds: While you lose the ability to turn into Super Sonic/Knuckles after depositing your Chaos Emeralds into Hidden Palace, you are still able to go to Doomsday Zone and still get the good ending.

And something about locking on other games to Sonic & Knuckles: The special stage you'll get from locking on the game is determined by its internal header. Also, the locked-on game must not exceed 16 megabits (that's 2,048KB) in size. If you try to lock on a game larger than that, like Sonic 3D Blast or Earthworm Jim, then you won't get any special stages, and S&K will boot as if you hadn't locked on any game. Why does it do that? Well, when locking on a game, the S&K cart only uses the last 2MB of the locked-on game and searches the mapped data for a header. If a game bigger than 2MB is locked-on, then S&K will read the last 2MB, find no header, then behave as if it was inserted into the console on its own. This only happens on real hardware, as emulators always read the first 2MB of a ROM.

An interesting note is that locking on Sonic Compilation on real hardware will activate the full version of Blue Sphere since Sonic 1 is at the end of the Sonic Compilation ROM. I think SEGA did that on purpose.

I think the game developers got bored one day while creating sonic and knuckles and said " hey, how about we create 134,217,728 special stages, just to irritate people."

once, i played blue sphere for 3 hours straight. all I could do after that was make 90 degree turns. D:

the thing with S3&K is that it's the first sonic game with an in-depth storyline. you can tell what's happenig and eventually the guy you thought was the bad guy was the good guy and the guy he thought was the good guy was the bad guy. In other words, there was a plot twist. Knux thought eggman was the good guy and sonic thought knuckles was the bad guy. But then eggman steals the M.E. and knux realizes that ol' eggy was the bad guy.

Wow. This was really over-elaborate.