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        riddles >> easy >> City Bloxx
        
(Message started by: JiNbOtAk on Oct 20^th, 2010, 4:08am)

Title: City Bloxx
Post by JiNbOtAk on Oct 20^th, 2010, 4:08am

I was getting hooked up with this mobile game, maybe some of you are familiar with it.

You are given a 5 x 5 grid, with 4 different towers that you can build, blue, red, green and yellow. You can place the blue tower anywhere, the red, however, must have at least one blue tower as a neighbour, the green, one red and one blue, and the yellow one blue, red and green. Needless to say, the yellow tower yields the highest amount of occupants, followed by green, red and blue.

Now, assuming your tower building skill is consistent, how would you place the towers to get the highest number of population ? What's the best configuration to ensure the highest number of yellow towers ?

Here's a pic for you guys to get a better picture.
http://cybernetnews.com/wp-content/uploads/2008/01/tower-bloxx.png

Title: Re: City Bloxx
Post by towr on Oct 20^th, 2010, 5:38am

Neighbours are N,E,S,W? Or also NW, NE, SW, SE ?

Title: Re: City Bloxx
Post by SMQ on Oct 20^th, 2010, 8:01am

From the provided example, diagonal neighbors must count or threeof the towers (the yellow tower on the bottom border, the two red towers in the second-from-bottom row) would be placed illegally.

--SMQ

Title: Re: City Bloxx
Post by rmsgrey on Oct 20^th, 2010, 9:41am

Should we assume that any arrangement with one yellow tower is automatically better than any arrangement with no yellow towers? Or would we need to prove it?

Title: Re: City Bloxx
Post by towr on Oct 20^th, 2010, 10:06am

If it's like the online version, http://www.funny-games.biz/towerbloxx.html , it's just N,E,S,W, but you can replace buildings as well.

Here's the configuration of a top scorer: http://www.funny-games.biz/images/screen_high_scores/33695.jpg
(which obviously took some replacements)

[edit]
For what it's worth,
max possible score with above configuration: 86925 (easily achieved by modifying the flash file a bit ;) )
max gold tower (perfectly straight with ornamental rooftop): 5738
max green tower: 2677
max red tower: 966
max blue tower: 205
[/edit]

Title: Re: City Bloxx
Post by JiNbOtAk on Oct 20^th, 2010, 10:10pm

on 10/20/10 at 10:06:04, towr wrote:

If it's like the online version, http://www.funny-games.biz/towerbloxx.html , it's just N,E,S,W, but you can replace buildings as well.[/edit]

Yes, the neighbours considered are just N,E,W,S. However, assuming that you can't replace buildings, what would be the best arrangement ?

rmsgrey, since we're assuming a consistent building skill, then yes..one yellow tower would be better than no yellow tower. Of course, that's not always the case. Since building perfect towers gives you extra points, and smaller towers tend to be easier to build perfectly..maybe more perfect small towers is better than unfinished higher towers ?

Title: Re: City Bloxx
Post by rmsgrey on Oct 21^st, 2010, 8:58am

on 10/20/10 at 22:10:48, JiNbOtAk wrote:

rmsgrey, since we're assuming a consistent building skill, then yes..one yellow tower would be better than no yellow tower. Of course, that's not always the case. Since building perfect towers gives you extra points, and smaller towers tend to be easier to build perfectly..maybe more perfect small towers is better than unfinished higher towers ?

Even without lower grade towers being better individually, it's possible to find arrangements with no yellow tower and lots of greens that potentially beat arrangements with one yellow tower and only one green...