DiMono
Level: Smitemaster
Rank Points: 1181
Registered: 09-13-2003
IP: Logged
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Re: Puzzle "tag" (0)
I have the solution (edited, as I found an error and changed my logic):
Everything that follows is based on what I have witnessed in game, and been able to create using the editor. Since the puzzle specs said different roach egg states can exist together, that's how I ran my logic.
If the 2x2 is taken up by a pillar (or tree, or whatever), then it can either be covered by tar or not. This is 2 combinations, since tar mothers cannot exist on obstacles. It could also be taken up by 15 combinations of tar babies (since no babies is the same as no tar), giving 17 so far.
There are some floor types that can only be inhabited by wraithwings:
9 pits without wraithwing
72 pits with wraithwing
(8 force arrow directions, 8 wraithwing orientations)
This gives 81 possibilities that can only be inhabited by wraithwings
There are some floor types that can only be inhabited by tar babies:
9 crumbly walls without tar baby
9 crumbly walls with tar baby
9 red doors without tar baby
9 red doors with tar baby
9 blue doors without tar baby
9 blue doors with tar baby
9 green doors without tar baby
9 green doors with tar baby
9 walls without tar baby
9 walls with tar baby
(these 9s come from different force arrow directions)
This gives 90 possibilities that can only be inhabited by tar babies
There are types of floor that can be inhabited by anything not a snake:
9 floors
9 trapdoors
9 open doors
9 closed doors
(8 force arrow directions)
8 scrolls (5 doors, crumbly walls, trapdoors, open floor)
This gives 44 open floor types
There are 5 monsters with 8 different orientations:
Wraithwing
Goblin
Roach
Roach Queen
Evil Eye
There are 3 monsters with 1 orientation:
Spider
Tar Baby
Brain
This gives 43 monsters that can be on those 44 open floor types, which is 1892 combinations
There are types of floor that cannot be inhabited by anything, that don't have tar:
orb
8 mimic potions
8 invisibility potions
(these 8s come from the five doors, crumbly walls, trapdoors, and open floor)
This gives 17 uninhabitable areas
Finally, roach eggs can exist in 3 states, only on open floor. Since the specs for the question say they can all exist independently from each other, I'll treat them like any other square
(checkpoints not included)
This gives 2091 total combinations, not including Beethro, snakes or tar. Since there are 4 squares, the total combinations of these combinations is 2091*2091*2091*2091, which is 19116841142961
If there is a complete tar mother in the area, it is either in the top half or the bottom half. This means we can take orientations for one of these, and multiply by 2. A tar mother can be on the following floor types:
floor
trap door
open yellow door
closed yellow door
This means there are 4 options for each square under the tar mother, which leaves 4*4=16
Ignoring snakes and tar, there are 2091 possibilities for each of the other 2 squares, so we take 16*2091*2091 with the tar mother in the top, then double it since the tar mother could be in the bottom. This adds 139912992 to our answer.
Supposing there's a snake of length 2 in with the tar mother:
It can either face left or right, and each square can either be floor, trap door, open yellow door or closed yellow door. This leaves 4*4 for the floor, *2 for the snake orientation, *16 for the tar mother gives 512*2(tar mother in top or bottom) = 1024 added to our answer
Supposing there's tar in the other 2 squares:
Tar can be on anything except pit, which is 10 possibilities. 10*10*16(mother)*2(mother location) gives 3200 added to our answer
Now, supposing there is a snake but no tar mother. The snake can either be 2, 3, or 4 long, in 8 orientations in each case. This means we can calculate the possible combinations for each length in a given snake orientation, then just multiply the numbers by 8 for the actual total.
Snakes can be on 4 square types:
floor
trap door
open yellow door
closed yellow door
If the snake is length 4, this is 4*4*4*4*8(orientation) gives 2048
If the snake is length 3, this is 4*4*4*2091*8(orientation) gives 1070592
If the snake is length 2, this is 4*4*2091*2091*8(orientation) gives 559651968
This is a total of 19117541784802 combinations
One last thing still unconsidered is the possibility of a stray tar mother eye. There are 8 possible ways for this to happen: left/right eye in one of the 4 corners. This gives the following, which will all be multiplied by 8 at the end:
Tar mothers can still only exist on 4 types of square.
If the rest of the room is a snake, this gives 4*4*4*4*2(snake orientation) which is 512
If the room has a snake of length 2, this gives 4*4*4*2091*2(snake direction)*2(snake position) which is 535296
If the room has no snake, then excluding tar this gives 4*2091*2091*2091 which is 36569758284
Since there cannot be stray tar, if it's present then it must occupy the other 3 squares. This gives 4*10*10*10 which is 4000
This means the number getting multiplied by 8 is 36570298092, which gives 292562384736
Adding the underlined numbers together gives us 19410104169538 absolute total combinations.
Assuming 60 minutes to an hour, 24 hours to a day, and that a year is 365.2425 days, it would take 38,820,208,339,076 minutes to do this all, or 647003472317.96666... hours, or 26,958,478,013.2472222... days, or 73,809,805.8502151918854520550653941... years for the workers to finish
[Edited by DiMono on 01-11-2004 at 10:05 PM GMT]
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/dy
