(no luck searching this topic, my apologies if it's already covered somewhere)

I've found something odd: adding a new link between goo balls costs a ball, and you get those extra balls back if you later break that link.

But the same structure can cost more or fewer balls based on whether you add links later or not.

For example, make this simple structure:



It costs 20 balls to make: I did it with 16 balls and had to add four more to complete missing links. (Is that optimal?)

But then remove one of the middle balls:



I got one ball back, so this 2nd picture costs 19 balls.

Now, to get back to the 1st picture costs FIVE balls! One for the ball itself, plus 4 more to recreate the missing links. Removing that center ball again gets you all five back, but menwhile they're... wasted balls? I can't find any difference between the two structures. It's not like those links that "cost a ball" instead of being "free" aren't any stronger or weaker... it just winds up reducing your available balls.

so for maximizing towers, this seems like a possibly important resource management issue.

Any thoughts?

it's in the whole game.  If a goo is able to make a new whole triangle, it will.  If it can't only make a link it will.  If it can do both it will alternate depending on where your mouse curser is. 

But yeah, it's always most efficient to make new triangles, if you can.  But there's some instances where you can't no matter what.  Plus different colored balls will react different.  IE in game a green ball will make (as far as I know) unlimited links.  A black/grey ball will only link up to two times.

[quote author=Pants link=topic=673.msg4910#msg4910 date=1225587130]It costs 20 balls to make: I did it with 16 balls and had to add four more to complete missing links. (Is that optimal?)I think that is indeed optimal. I've been trying to make a theory for predicting the minimum, but I keep messing it up. Something with how many balls your starting edge needs or something. :/

How did you guys arrive at 20 balls? Since you can't start structure from nothing, I assume you started from an existing shape, attached goos to it, and then demolished the supporting structure.

So you would for example start with a triangle, build it like this:
[pre]
          O---O---O
        / \ / \ / \
        O---O---O---O
      / \ / \ / \ / \
  *---O---O---O---O---O
/ \ / \ / \ / \ / \ /
*---*---O---O---O---O
[/pre]
and then tear up the goos marked with an asterisk.

If we don't count the triangle you need to add 16 nodes and 37 edges. Every goo ball either becomes a node and two edges, or just a single edge, and since removing a node removes all adjacent edges, an optimal building strategy must use exactly 16 nodes to create 32 edges, which leaves 5 edges to be added by single goos. So that would give a lower bound of 21 goo balls, not 20.

Did I understand the example wrong? Can one of you give an example of how to build up the structure with only 20 goos?

Hmm no I think you're right, I counted the first edge of a starting triangle as using 1 goo, but you need 2 goos. Which is probably why my theoretical predictions kept failing to comply with my view of reality.