Tower of Babel Forum

Dr. · Administrator Messages: 310 Location: Saarbrücken

You know... sometimes I think the time has come when every possible innovative tower has been built. Every trick tried. Every loophole exploited. Every trap sprung. Every combination of elements tried.

Do we really need new elements, or am I just lazy?

--
Das Lemsche Gesetz:
Niemand liest etwas; wenn er etwas liest, versteht er es nicht; wenn er es versteht, vergißt er es sofort.

Fawlty · Mason Messages: 280 Location: Gütersloh

Very difficult topic. First of all, no, not every innovative tower has been built yet. Just remember how quick we came up with some REALLY good new towers after we re-discovered ToB! And different people always have different ideas. I'm pretty sure we'll see some interesting new levels at least when the remakes are finished.
The first (and second) wave of euphoria is gone, of course. I haven't done anything ToB-related in the last few weeks, and judging from the activity in the forum, I'm not the only one who's gotten a little lazy lately.
But we're still fans, we're still longing for the remakes, and we'll still sacrifice a couple of brain cells trying to puzzle out new towers to torture the rest of us.

Concerning new tower elements, I absolutely agree with what you posted in the ToB2 forum. If they are not chosen wisely, they can destroy more than they can improve. In my opinion we must not introduce anything to the game that disturbs its original ways and ideas. But some fresh blood, well-balanced and adequate, should be nice anyway.
There already had been some promising ideas in the remake-threads, and we should revive those discussions to pick the best ones.

Dr. · Administrator Messages: 310 Location: Saarbrücken

I don't know... Perhaps I've just run out of original ideas, but every tower starts to look like some old tower I've already built or seen. Nothing really new or inventive I can come up with.
But, hey, variation is an art form in itself, right? And I'm sure other people can come up with things I've never thought of yet.

--
Das Lemsche Gesetz:
Niemand liest etwas; wenn er etwas liest, versteht er es nicht; wenn er es versteht, vergißt er es sofort.

Artinum · Zapper Messages: 184 Location: United Kingdom

There IS a limited number of towers that can be made. One is limited to just 8x8x4 spaces with only 5 basic elements (blank, floor, block, up-lift, down-lift) that can be included (less than that, really, but the maths gets complex and I'm only after an upper boundary). So (before you put objects and spiders in) there are less than 1280 towers you can make. This includes impossibilities such as up-lifts on the top and spaces on top of blocks, not to mention Fawlty's weird towers.

We'll ignore the cosmetic aspects of towers, as the only effect colour changing would have is to do evil things like hide lifts or plunge the tower into darkness.

Objects make the tower fun. You can have one, two or three spiders in the game (seven ways to do this - Z, P, G, ZP, ZG, PG, ZPG - as no spiders makes no sense) and 0-17 other objects from a range of let's say 40, including different facings etc. (because I can't be bothered to count them). Let's assume this 40 includes a 'null' object if we have less than 17 in the tower, so we can now state we have 40x17 ways of choosing these objects, or 680. Multiply this by the separate issue of spiders and we have 4760 possibilities.

We can place these objects anywhere on a tower. Ignoring the location of floors and the possibility of two objects coinciding there are just 8x8x4 floor locations, so each object has a potential 256 locations, including the spiders. The result is 256^20 possibilities, at which point I break out the calculator and discover it's less than 1.4615016373309029182036848327163e+48 (1.5 decapentillion(?)).

I'll skip finishing conditions and a time limit, as they are fairly irrelevant here. I will, however, include the option of mines destroying the floor and the three speeds for time bombs.

So the total number of possible towers is considerably less than my upper bound of 5.3427823055578351800188465692632e+55 towers, many of which are going to be duplicated and many more of which are impossible to even construct.

A finite, if large number!

First person to construct them all wins a fiver...

Artinum.

chrizb · Pusher Messages: 62 Location: london

Hi,

Interesting calculations, but probably (as you pointed out) including some redundancies. Here is a start:

a) single tile levels (5120)
b) symetrical levels ( only every 4th level is unique)
c) single floor level repeats on different levles (/3)

but I think there might also be another factor (although maybe Artinum is right when saying "I'll skip finishing conditions and a time limit, as they are fairly irrelevant here") which reduces the number

d) level with undoable finishing conditions (calculation of this is somewhat harsh, but it is likely to be 50% or more.
e) Object only levels should also be avoided (256^2) might be a good estimate here.

even taking all this into account, there is more levels to build than you can look at in a lifetime (3,155,760,000 = 1 level /sec for 100 years)

But is that enought? Or is there a need to spice up the puzzles?

Maybe have a realtime element
3 vs 3 online (whoever finishes the level first wins?)
New elements (carefuly selected and tested, not to upset the balance)
New players
play chess

Have fun

looks can be deceiving

Fawlty · Mason Messages: 280 Location: Gütersloh

Zitat: Artinum

... So (before you put objects and spiders in) there are less than 1280 towers you can make. ...

I just hope you don't need any math for your job. *g*
Let's make things a little simpler and say that a tower has only 5 spaces and 2 basic elements. Using your calculation, that makes 10 towers, ignoring objects etc.
Now simply count the possibilities, and reconsider your math...

Artinum · Zapper Messages: 184 Location: United Kingdom

Ooops. You're right. I was rushing through stuff a little at the time. Rather than there being 8x8x4x5 combinations for towers, there are in fact 5^(8x8x4) combinations, or 5^256. Rather bigger than 1280...

Oh well. It makes all the numbers much bigger but they still ain't infinite. Fair enough regarding all those ways to trim down the number of towers but since there aren't many simple ways to do them, and more importantly because the actual number doesn't matter much, there's little point here.

As for symmetry, that is true. But rotational symmetry can't be ignored - the facing direction for many objects is crucial. A lizard always starts by going north, for instance, so put him at the end of a row of tiles and he'll eat the first one straight away if it's the north end.

Finishing conditions are a good question. I decided to focus on the towers themselves rather than the conditions and time limit because, if you've got a tower with X klondikes and Y destroyable objects, there aren't that many ways to vary things. Time limits in particular are strange - you could theoretically have a tower with 1-9999 second time limits or no limit but a single second wouldn't make two different towers. In the end time limits are the sort of thing you assign at the end with fine tuning.

Ultimately, most of these towers are impossible to even create in the editor (Zapper in midair?) and of the others, tons would be either boring, unplayable or pointless. Imagine Grabber in a sea of klondikes. Or Grabber cut off from a sea of klondikes. Or a level with all three spiders in a featureless tower with no objects at all.

Artinum.

Dr. · Administrator Messages: 310 Location: Saarbrücken

Aah, but how to quantify the interest factor? No matter how many blocks I put on four levels in all kinds of kombinations, unless there's an interesting puzzle it all falls flat...

--
Das Lemsche Gesetz:
Niemand liest etwas; wenn er etwas liest, versteht er es nicht; wenn er es versteht, vergißt er es sofort.

Artinum · Zapper Messages: 184 Location: United Kingdom

Well exactly. I daresay of the millions of possible, playable towers about 85% of them probably turn out to be mazes of some kind. Yawn.