Math Probability Question

GoodSelf

Zhu Li! Do the thing!
Veteran
Joined
Jul 23, 2016
Messages
598
Reaction score
1,134
First Language
English
Primarily Uses
RMMV
Alright, so lets say that I have 9 tiles arranged in a 3x3 pattern.
Each of these tiles has 3 possible variations, lets say they can be either Red, Blue, or Green.


It's easy for me to find out how many combinations there are, its simply 39 or 19,683 possible combinations.


Now, lets say that I divide the tiles into three groups, with 3 tiles each. (This is where it get's confusing).
Now instead of each tile having a Red, Blue, or Green condition randomly, it is now fixed (meaning that you will never get multiples of a color in that set of 3).


An example is in the spoiler below.

If Tile 1 is set to Red, then Tile 2 will be automatically set to Green, and Tile 3 set to Blue.
If Tile 1 is set to Green, then Tile 2 will be automatically set to Blue, and Tile 3 set to Red.


If Tile 1 is set to Blue, then Tile 2 will be automatically set to Red, and Tile 3 set to Green.



With this new fixed system, how many combinations of tiles can I achieve in a 3x3 space? 


What kind of formula would I use to figure this out?
 
Last edited by a moderator:

bgillisp

Global Moderators
Global Mod
Joined
Jul 2, 2014
Messages
13,787
Reaction score
14,582
First Language
English
Primarily Uses
RMVXA
It's way lower. The first tile can be anything, so there are 3 choices for it. The 2nd tile can be anything but the 1st tile's color, so there are 2 choices for it. The 3rd tile has 1 choice, as it has to be the only color left. That is 3 * 2 * 1 or 6 choices per set of 3.


Since each set of 3 is independent, it is 6 * 6 * 6 = 216 total choices. It gets even lower if you decide you want tile 1 in set 1 and tile 2 in set 1 to not be the same.


But it was all multiplication rule, just had to exclude the cases that no longer mattered.
 

chungsie

Veteran
Veteran
Joined
Sep 9, 2015
Messages
656
Reaction score
858
First Language
English
Primarily Uses
N/A
ya I was beat to the punchline... also if you needed alternatives to your rules, one could use a Power Set function I would think.
 

Shaz

Global Moderators
Global Mod
Joined
Mar 2, 2012
Messages
42,127
Reaction score
14,643
First Language
English
Primarily Uses
RMMV
nah, it's even easier than that, because the second and third tile in each group won't choose between colors..


You're saying if tile 1 is color 1, then tile 2 WILL be color 2, not that it can either be color 2 or 3.  So each group of 3 only has 3 possible outcomes, not 6: 3x1x1, rather than 3x2x1.


Since each group is independent, you have 3 possibilities for group 1, 3 for group 2 and 3 for group 3.  3x3x3 = 27.
 

bgillisp

Global Moderators
Global Mod
Joined
Jul 2, 2014
Messages
13,787
Reaction score
14,582
First Language
English
Primarily Uses
RMVXA
@Shaz: That's if you use the fixed examples provided. I assumed it could take on either of the two remaining colors, and read those as examples only. But yes, if you force it into that pattern, then it is 27 like you said.
 

Latest Threads

Latest Profile Posts


Finally done with the school project, here's the raw video of it. o_O :smile:
Can February March? No, but April May.
Alisa: Prophecy of the Falling Stars. Join Alisa, a quiet girl with a heart filled with love and hope, on her journey to prevent a calamity. My next RPG Maker music pack is my largest and most focused pack yet. It's a musical story that focuses on a young heroine named Alisa who has been assigned the ultimate task to prevent a calamity.

SnJj_O.png

Forum statistics

Threads
111,166
Messages
1,058,906
Members
144,413
Latest member
MrPoporucha
Top