Mister
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agaricus5 wrote:Tar mothers do not go on yellow doors. I\'ve re-corrected the chart.

No, the mistake is in your alignment of the top line. You actually modified the \"Serpent\" column.


EDIT: new topic page, new table.

              Rch RQn REg Wrt Eye Gbl Spd Brn Bby Non   TOT   Srp Tar Mot
==========================================================================
Floor          8   8   3   8   8   8   1   1   1   1  |  47 |  Y   Y   Y
Scroll         8   8           8   8           1   1  |  34 |
Trapdoor       8   8       8   8   8   1       1   1  |  43 |  Y   Y   Y
Arrow         64  64      64  64  64   8       8   8  | 344 |
Arrow/Trap    64  64      64  64  64   8       8   8  | 344 |
Yellow Open    8   8       8   8   8   1       1   1  |  43 |  Y   Y
Yellow Closed  8   8       8   8   8           1   1  |  42 |  Y   Y
Pit                        8                       1  |   9 |
Wall                                           1   1  |   2 |      Y
Other door                                         3  |   3 |
Arrow/Pit                                          8  |   8 |
Potion                                             2  |   2 |
Scroll/Trap                                        1  |   1 |
Crumbly Wall                                       1  |   1 |
Orbs                                               1  |   1 |
==========================================================================
             168 168   3 168 168 168  19   1  23  39    924
                Number of \"Tar may have existed\" tiles: 186

This will be the Ultimate Drod Combination Table.
Any mistake, please just point it out to change it and avoid spamming with lots of tables.


[Edited by Mister on 04-24-2003 at 11:19 PM GMT]

agaricus5
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I can't believe that I've had no solutions for this since 23/04/03!

If you have submitted an answer previously, please re-send it so I know about it.

And Schik... I can't remember... what was your solution again?




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Mister
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Sokko
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To get leap years, just divide the number of years by 4 and add that number of days, adding a year when you go over 365. For every 4 years you add in this manner, add an extra day. (because every 1 out of 4 years you create using the days from leap years are going to be leap years too)

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Schik
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Sokko wrote:
To get leap years, just divide the number of years by 4 and add that number of days, adding a year when you go over 365.

Just divide the number of days by 365.24 (A leap year is every 4 years, except every 100 years, IIRC).


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bdcribbs
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Years evenly divisible by 4 are leap years, with the exception of 00 years that are not divisible by 400.
Since the cancelled leap year returns once every 400 years add 0.0025 days to bring the average to 365.2425 days per year.

Mister
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I didn't add leap years (nor leap seconds, either) because I don't know the starting date of the question

[Edited by Mister on 05-09-2003 at 05:13 AM]

mrimer
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Hehe. Hey, that's right! I guess... (I'm still waiting for that last remark to be followed by a funny laugh like Ernie from Sesame Street makes, or something.)

Okay, Erik. What's the year when the latest chapter of "Beethro the Delver" is taking place?

[Edited by mrimer on 05-09-2003 at 05:22 AM]

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Mister
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And more important:
Has Gregorian Calendar been invented yet?

mrimer
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Mister wrote:
And more important:
Has Gregorian Calendar been invented yet?

Heh. We don't have to assume that Dugandy is in the same land, culture, or world that we live in. Why would they have the same dating systems as we do at all?

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agaricus5
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True, but I assumed that they'd have the 24 hour day, just like we do, which is why I said each arrangement took 2 minutes to set up.

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agaricus5
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This has been a little quiet lately... maybe people aren't interested anymore? :~)

However, the "years" problem has been more or less sorted out; see the bottom of this page of thread:

http://www.drod.net/forum/viewtopic.php?TopicID=368&page=2

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Mister
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I stopped following that topic long ago...

Anyway, the starting time isn't specified (or is it?)


Supposing they start at 8:00 am, Novender 36th of year 147 B.D., all combinations will be done at 4:04 pm, Onsuary 23th of year 3041085 B.D.

[Edited by Mister on 06-26-2003 at 10:18 PM]

eytanz
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agaricus5 wrote:
This has been a little quiet lately... maybe people aren't interested anymore? :~)

I don't think this thread can quite compete with the attraction of the beta - probably as things wind down on that front, people will return here.

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I have the solution:

Everything that follows is based on what I have witnessed in game, and been able to create using the editor


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)
This gives 36 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 36 open floor types, which is 1548 combinations

There are types of floor that cannot be inhabited by anything, that don't have tar:

orb
8 scrolls
8 mimic potions
8 invisibility potions
(these 8s come from the five doors, crumbly walls, trapdoors, and open floor)
This gives 25 uninhabitable areas

(checkpoints not included)

This gives 1744 total combinations, not including Beethro, snakes or tar. Since there are 4 squares, the total combinations of these combinations is 1744*1744*1744*1744, which is 9250941239296


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 1744 possibilities for each of the other 2 squares, so we take 16*1744*1744 with the tar mother in the top, then double it since the tar mother could be in the bottom. This adds 97329152 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*1744*8(orientation) gives 892928

If the snake is length 2, this is 4*4*1744*1744*8(orientation) gives 389316608


This is a total of 9251428784273 combinations without roach eggs.


Roach eggs exist in 3 states, and can only spawn on open floor without arrows. I'll assume that all eggs exist in the same state at the same time, as happens in the game.

In a room with a snake 3 long, this means there are an extra 3 * 8 possibilities, which adds 24 to the total.

In a room with a snake 2 long, this means there are an extra 1744*3*8 possibilities, which adds 41856 to the total

In a room with a tar mother, if there is 1 roach egg this adds 1744*3*2(queen location) possibilities, which adds 10464 to the total

In a room with a tar mother, if there are 2 roach eggs this adds 6 possibilities to the total

In any other room, this is just a different state for the squares. If there is 1 roach egg included, this adds 1744*1744*1744*3*4(roach egg location) to the total, which is 63653265408

If there are two roach eggs included, this adds 1744*1744*3*6(roach egg locations) to the total, which is 54949648

If there are 3 roach eggs, this adds 1744*3*4(non-roach egg location) to the total, which is 20928

If all 4 are roach eggs, this is another 3 added.

And so, including roach eggs there are 9315137072610 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*1747(including 3 roach egg states)*2(snake direction)*2(snake position) which is 447232

If the room has no snake, then excluding roach eggs and tar this gives 4*1744*1744*1744 which is 21217755136

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

If there are roach eggs, the following can exist:

With 1 egg, we have 4*1744*1744*3*3(egg location) which gives 109495296 (without snakes, since they've already been covered above)

With 2 eggs, we have 4*1744*3*3(non-egg location) which gives 62784

And if all 3 are eggs, we have 4*3 which is 12

This means the number getting multiplied by 8 is 21327800972, which gives 170622407776

Adding the underlined numbers together gives us 9485759480386 absolute total combinations. If you allow roach eggs to be in any state together, then you change all the 1744 to 1747 and remove the independant roach egg sections, as they then become just another square.


Assuming 60 minutes to an hour, 24 hours to a day, and that a year is 365.2425 days, it would take 18,971,518,960,772 minutes to do this all, or 316,191,982,679.53333... hours, or 13,174,665,944.9805555... days, or 36,071,010.2054951314689707675189923... years for the workers to finish

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Mattcrampy
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eytanz wrote:

agaricus5 wrote:
This has been a little quiet lately... maybe people aren't interested anymore? :~)

I don't think this thread can quite compete with the attraction of the beta - probably as things wind down on that front, people will return here.

Irony is fun, isn't it?

Matt

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agaricus5
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I don't think that's right. Use the UDCT at the top because the puzzle was created before the editor, so some placements are disallowed in this puzzle. Also, Tar babies, Roach Eggs and Spiders are non-rotateable. One other thing. There are eight orientations of monsters, not nine.

Edit: Actually, since the editor has come out, ignore the UDCT.

I'll make a list of all possible combinations again in a little while.

[Edited by agaricus5 on 01-11-2004 at 09:40 PM GMT]

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DiMono
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Who ever said there were 9? There are 9 states of arrows, the 8 directions or absent. Monsters are multiplied against that. ( 5*8 + 3*1 ) * ( 4*9 )

I'd also like to say that, given that we now have the editor and the different orientations, I feel it's unfair to ask us to use a version of DROD we don't play any more. We have access to AE, so why not use AE?

I did find an error in my calculations though, which I'll correct

[Edited by DiMono on 01-11-2004 at 09:46 PM GMT]

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DiMono
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I have the solution (again):

Everything that follows is based on what I have witnessed in game, and been able to create using the editor. Last time I forgot that creatures can exist over scrolls, and I decided to conform to what was specified above about roach eggs being able to exist in different states together


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

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agaricus5
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DiMono wrote:
Who ever said there were 9? There are 9 states of arrows, the 8 directions or absent. Monsters are multiplied against that. ( 5*8 + 3*1 ) * ( 4*9 )

I'd also like to say that, given that we now have the editor and the different orientations, I feel it's unfair to ask us to use a version of DROD we don't play any more. We have access to AE, so why not use AE?

I did find an error in my calculations though, which I'll correct

[Edited by DiMono on 01-11-2004 at 09:46 PM GMT]

OK.

I'll adapt my solution (Re-do it). Please wait for my update as there are some things I don't want to allow because they are not logical, e.g. Roaches on walls or green, red or blue doors.

[Edited by agaricus5 on 01-11-2004 at 11:27 PM GMT]

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agaricus5
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File: Placement Rules.xls (16 KB)
Downloaded 79 times.
License: Other
From: Unspecified

Ok.

I've just re-done it.

From what I've done, you'll have to re-calculate once more, DiMono. I'm sorry.

Here are the placement rules in very rushed form.

Specific Notes:

Nothing can go on a wall except Tar and Tar babies
Nothing can start/go onto a Potion.
Only Potions, Force Arrows, Scrolls, Tar and Tar Babies can go onto a Crumbly Wall.
Only Potions, Force Arrows, Scrolls, Tar, Tar Mothers and Tar Babies can go onto a Red, Blue or Green Door.
Roach Eggs can exist in all different stages at once, but can only exist on normal floor.
Tar can't go on Force arrows or Scrolls, so Babies cannot exist on [Crumbly walls or Walls with Force Arrows or Scrolls on them] or [Doors with Scrolls or Force Arrows on them]

Apologies for the slightly unclear presentation (It mirrors the unclearness in my head - I need sleep!)

[Edited by agaricus5 on 01-12-2004 at 12:43 AM GMT]

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DiMono
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Tar babies can't move to walls or crumbly walls with force arrows, but they can start there, thus making their placement legal.

Just out of curiosity, did you get more than me or less than me when you recalculated, and was it a significant amount or a non-significant amount?

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agaricus5
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DiMono wrote:
Tar babies can't move to walls or crumbly walls with force arrows, but they can start there, thus making their placement legal.

Check the attached file for the arrangements I'm allowing. I think you've allowed Tar Babies on Red, Green or Blue Doors with Force Arrows on them, which is wrong - there are only two arrangements of Tar Babies and Red, Blue or Green Doors - either no tar baby exists on it, or there is one on it. Although it is theoretically possible to get an arrangement where a baby is on a Green door with a force arrow, you can't place a baby on a Green door in the Editor, and you can't place Tar on a force arrow. So for this puzzle, it's not possible.

I'll let you have another go, and then I'll reveal my answer.

Just out of curiosity, did you get more than me or less than me when you recalculated, and was it a significant amount or a non-significant amount?

Less, and by a very large amount.

[Edited by agaricus5 on 01-12-2004 at 09:23 AM GMT]

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agaricus5
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DiMono wrote:
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

This is also incorrect, for we are in the Eighth.

Go see this thread for the "new" calendar that Eighthers use:

http://www.drod.net/forum/viewtopic.php?TopicID=368&page=2


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DiMono
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agaricus, your spreadsheet fails to take in to account that there are fifteen combinations of tar babies on a pillar.

It also seems that our copies of DROD allow us to do different things in the editor, because I specifically tested placing a tar baby on an arrowed green door, and it worked fine. I'll attach a demo hold when I get home.

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agaricus5
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DiMono wrote:
agaricus, your spreadsheet fails to take in to account that there are fifteen combinations of tar babies on a pillar.

The spreadsheet only covers possible combinations. Other Tar and Serpent calculations need to be worked out by hand. I wouldn't just give you the answer now, would I?

It also seems that our copies of DROD allow us to do different things in the editor, because I specifically tested placing a tar baby on an arrowed green door, and it worked fine. I'll attach a demo hold when I get home.

That's pure oddness. We must submit the bug if we have differences. Can you place monsters on potions?

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DiMono
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File: tar babies.hold (1.4 KB)
Downloaded 79 times.
License: Other
From: Unspecified

Alright, I've played around in the editor again, and here's what I now have without using the spreadsheet, since I don't have excel handy. I've attached a two room hold I used to test some combinations, just to show that I'm not inflating my numbers. As it is, I think it's not solvable, so save your time :

Pillars can either be empty, covered in tar, or have any of 15 combinations of tar babies, giving 17 combinations off the top

Now we need to figure out our basic list of tile types. Orbs must be on regular floor, and cannot be inhabited, so that's 1 so far.

Pits come in these states:

1 empty
8 arrows
64 combinations of arrows and wraithwings
8 wraithwing orientations on a normal pit

That's another 81 options so far

The following can only be inhabited by tar babies:

wall
crumbly wall
green door
blue door
red door

Each of those can also be empty and have force arrows, so that's 10 of each. Everything except walls can also have scroll or the 2 potions, so that's 13 of those, adding 62 to our total options

Alright, the nitty gritty. The following can have any creature not a serpent, tar mother or roach egg on them:

12 trapdoors
12 floors
12 open yellow doors
12 closed yellow doors
(normal, 8 force arrows, 2 potions, scroll)
That would add 48 to our total options, but we can't have open and closed yellow doors next to each other. For now, let's add 24, and we'll deal with having yellow doors later.

These creatures can appear on those spaces:

8 goblins
8 wraithwings
8 roaches
8 roach queens
8 evil eyes
1 tar baby
1 spider
1 brain
1 empty

Which is 43 monster combinations. 44*24 is 1056
For later reference, the number of these combinations that may use closed yellow doors is 44*36=1584

Roach eggs can appear in 3 states on open floor only, so that adds 3 to our total

Tar mothers and serpents can appear on open floor, trapdoors, and open or closed yellow doors. We'll deal with these later.

So the number of tile types we have without yellow doors, tar, or serpents is 1227. Given these restrictions, we have 1227*1227*1227*1227 combinations, which is 266617569841

We can also have yellow doors, though, so we must account for those. The total number of tile options that can have a closed yellow door will be 1227-1056+1584(from above), =1755, which means the total combinations that may include closed yellow doors will be 1755*1755*1755*1755, from which we subtract the previous number to get the number of combinations that actually do include closed yellow doors. Then we double that, and that's the total combinations that include any yellow doors. The number of combinations that include closed yellow doors is 9219936430784, which we double to get 18439872861568. Adding this to the first number gives us a total of 18706490431409 combinations that don't have serpents or tar.

Let's now deal with tar mothers. If there is a tar mother, it may be accompanied by more tar. Tar can exist on the following (hence the reason tar babies can exist on them):

wall
crumbly wall
red door
green door
blue door
floor
trapdoor
open yellow door
closed yellow door

Again, let's ignore yellow doors entirely for now. If a complete tar mother is in the room, then ignoring yellow doors it can be on floor or trapdoor, so we have 2*2=4 combinations for the mother. The tar can be on any of 7 surfaces, and 7*7 = 49. 4*49=196

Now, if a closed yellow door is in the equation, we change the 2*2 to 3*3=9, and the 7*7 to 8*8=64, and multiplying them together gives 576 total combinations that may include a closed yellow door. Subtracting the number that don't have one (196) gives us 380 that do include closed yellow doors. Multiply by 2 to account for open yellow doors gives us 760, +196=956, *2 since tar mothers can be in the top or bottom half, so there are a total of 1912 combinations of tar mother with tar filling the rest.

If the rest is filled by snake, the calculation is trivial. We have 2*2 for the mother, and 2*2 for the snake, *2 for snake direction gives 32 combinations that don't include doors. Changing it to 3*3*3*3*2 gives us 162, -32=130 that include a closed yellow door, *2 to account for open gives 260 +32 = 292, *2 for tar mother location is another 586 combinations with a tar mother and a snake.

Now, if there is no snake, we have 2*2*1227*1227=6022116 combinations that don't have yellow doors. Changing it to 3*3*1755*1755 to get the number of combinations that may have closed yellow doors gives us 27720225 - 6022116 = 21698109 combinations that do have closed yellow doors, *2 to account for open yellow doors gives 43396218, + the original 6022116 gives 49418334 * 2 for tar mother position gives 98836668 total combinations with a tar mother and no snake or tar. This means the total combinations that have a complete tar mother is 98839166.

Now let's look at half tar mothers. There are 8 ways to have half a tar mother (4 positions * 2 eyes), so instead of multiplying our numbers by 2 we multiply them by 8. Without the snake, these numbers are easy to calculate from the earlier ones.

If the rest is filled by tar, we have 2*7*7*7=686 without yellow doors, 3*8*8*8=1536 that might have closed yellow doors, 850 that do have closed yellow doors, *2=1700 to account for open yellow doors, which gives 2386 *8 for tar mother orientation is 19088 combinations where the rest is tar.

If the rest is filled by snake, we still have 292 combinations without accounting for tar mother orientation. If two of the other squares are filled by snake, we have 2*2*2*1227=9816 combinations that don't have yellow doors, *2 for snake direction *2 for snake position=39264 combinations that have a snake of length 2 without yellow doors. changing it to 3*3*3*1755*2*2 gives us 189540 combinations that might have closed yellow doors, -39264 is 150276 that have closed yellow doors, *2=300552+39264=339816 with snakes length 2. Adding the 292 for snake length 3 and multiplying by 8 for tar mother orientation gives us 2720864 total combinations with half a tar mother and a snake.

Finally, if the rest isn't a snake we have 2*1227*1227*1227 for no yellow doors, giving us 3694568166 combinations with no yellow doors. Changing it to 3*1755*1755*1755 gives us 16216331625 that may have closed yellow doors, and 12521763459 that do have closed yellow doors. *2 for open gives 25043526918, +3694568166=28738095084, *8 for tar mother orientation gives 229904760672 total combinations with half a tar mother, and no other tar or snake. This means there are 229907500624 total combinations with half a tar mother.

Now, if there is tar but no tar mother, then we have 7*7*7*7 combinations without yellow doors is 2401. 8*8*8*8 gives 4096 that might have a closed yellow door, -2401=1695 that have closed yellow doors, *2 for open yellow doors gives 3390 that have yellow doors, +2401=5791 combinations that have tar but no tar mother.

Last thing to deal with is snakes but no tar. In all of these cases, we have *4 for head position and *2 for direction is *8, which I'll wait until the very end to do.

If it's a snake of length 4, we have 2*2*2*2=16 ways with no yellow doors, and 3*3*3*3=81 that might have closed yellow doors, so 65 that do have closed yellow doors, *2 for open +16 for none is 146 that have snakes of length 4.

If it's a snake of length 3, we have 2*2*2*1227=9816 that don't have yellow doors, and 3*3*3*1755=47385 that might have closed yellow doors, so 37569 that do have closed yellow doors. *2=75138 that have yellow doors, +9816=84954 that have snakes of length 3.

If it's a snake of length 2, we have 2*2*1227*1227=6022116 that don't have yellow doors, and 3*3*1755*1755=27720225 that might have closed yellow doors, so 21698109 that do have closed yellow doors, *2 for open yellow doors gives 43396218, + the original 6022116 gives 49418334 total combinations with a snake of length 2.

Adding the snake combinations together gives us 49503434*8=396027472 total combinations with a snake and no tar.

Adding the underlined numbers together, as those are our totals for each section, gives us 18,936,892,804,479 total combinations, and 37,873,785,608,958 total minutes spent setting them up. However many years and days that ends up being, that's my answer, I'm tired of doing math for this puzzle



Oh, and when I was playing around in the editor again I wasn't able to put tar babies on walls or closed doors, and I was able to put monsters on potions. Maybe I was just feeling silly or something, we'll never know.

____________________________
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RubellaGolda
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Fascinating, and yet tiring discussion this is.

Sokko wrote:
Not that I really know a lot about this stuff, but I think it would be pretty obvious that stages of roach eggs cannot coexist; it's impossible, because all queens use the same counter and there is no possible event that could offset one or more of them.

Tar mothers by themselves are perfectly plausible, because it is possible (albeit very difficult) in the game to cut away all the tar from a mother so there's nothing left but the eyes. By the same token, you could then chop off one of the eyes and have only one left. Or you could have two mothers right next to each other and chop off various parts of them; in short, all combinations of eyes should be possible. That's basically what Beethro (agaricus) just said... extended version.

BTW, why don't mothers with eyes closed count? It's perfectly reasonable, so long as all of the eyes in this 2x2 square are either closed or open.

If closed eyes count, they cannot exist together with roach eggs.

agaricus5
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File: UDCT.xls (19 KB)
Downloaded 239 times.
License: Other
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Having a proper editor to check the validity of the solution to this puzzle, I am now going to finish off this puzzle properly to get a solution that I think is accurate (DiMono, according to what I got, your answer is off by quite a lot). If there are no objections or errors, I will post a new, updated version of the puzzle to modernise it, clarify problems, and also remove some of that annoying commentary so rife in some of my older posts. To clarify the start date and time, I set it at Novender 37, 147 B.D 12:00 p.m.

Edit: The puzzle can be found here.

Attached to this post is my new copy of the UDCT (Ultimate DROD Combination Table). If there is a problem with it, then please tell me and I'll revise it and the solution. However, these placement rules are based on the fact that they can either be placed like this in the Editor at the start, or that they can be valid placements within a game. The exception is with Trapdoors beneath Orbs, which is obviously a bug.

So it can be found easily, I'm going to put the other UDCT (Ultimate DROD Combination Total ) at the top of the message for easy reading.

Using strict DROD rules (spawning events always happen in sequence):

The total is 27,342,500,886,157 different arrangements...

Which will take 54,685,001,777,314 minutes...

Or 114,041,128 years, 51 days, 5 hours and 14 minutes to set up.

If they began on Novender 37, 147 B.D, at 12:00 p.m., they would finish on Twisuary 13, 114,041,276 B.D, at 5:14 p.m.

Using non-strict Eighth rules (spawn events can happen at any time in the Eighth):

The total is 27,357,423,701,047 different arrangements...

Which will take 54,714,847,402,094 minutes...

Or 114,103,368 years, 263 days and 54 minutes to set up.

If they began on Novender 37, 147 B.D, at 12:00 p.m., they would finish on Octender 3, 113,103,516 B.D, at 12:54 p.m.

My Working Out:

Case 1. All single-square monsters and elements, except eggs and Tar Mothers:

Total - 2256^4 = 25,903,376,695,296

Case 2. All single-square monsters and elements, except Tar Mothers, where at least one is an egg:

1. Strict DROD rule version - Eggs are always the same age.

For 1 egg - 4 * 3 * 2256^3 = 137,783,918,592
For 2 eggs - 6 * 3 * 2256^2 = 91,611,648
For 3 eggs - 4 * 3 * 2256 = 27072
For 4 eggs - 3
Total - 137,875,557,315

2. Non-strict Eighth rule version - Eggs can be of different ages.

For 1 egg - 4 * 3 * 2256^3 = 137,783,918,592
For 2 eggs - 6 * 3^2 * 2256^2 = 274,834,944
For 3 eggs - 4 * 3^3 * 2256 = 243,648
For 4 eggs - 3^4 = 81
Total - 138,058,997,265

Case 3. - The 2*2 tar mass, without Tar Mothers or a Pillar as the floor square:

Total - 9^4 = 6561

Case 4. - The 2*2 tar mass, with at least one Tar Mother eye, but no Pillars as the floor square:

1. Strict DROD rule version - The eyes of the Tar Mothers must all be in the same state.

For 1 eye - 4 * 14 * 2 * 9^3 = 81,648
For 2 eyes - 6 * 14^2 * 2 * 9^2 = 190,512
For 3 eyes - 4 * 14^3 * 2 * 9 = 197,568
For 4 eyes - 14^4 * 2 = 76,832
Total - 546,560

2. Non-strict Eighth rule version - Tar Mother eyes can be at different stages.

For 1 eye - 4 * 28 * 9^3 = 81,648
For 2 eyes - 6 * 28^2 * 9^2 = 381,024
For 3 eyes - 4 * 28^3 * 9 = 790,272
For 4 eyes - 28^4 = 616,456
Total - 1,867,600

Case 5. - 1-3 Tar Mothers, but not in a tar mass, with all single-square objects and monsters.

1. Strict DROD rule version - The eyes of the Tar Mothers, and eggs must all be in the same state, and eggs cannot exist if the Tar Mother's Eyes are closed.

For 1 eye, 0 eggs - 4 * 14 * 2 * 2256^3 = 1,285,983,240,192
For 1 eye, 1 egg - 4 * 14 * 3 * 3 * 2256^2 = 2,565,126,144
For 1 eye, 2 eggs - 4 * 14 * 3 * 3 * 2256 = 1,137,024
For 1 eye, 3 eggs - 4 * 14 * 3 = 168
For 2 eyes, 0 eggs - 6 * 14^2 * 2 * 2256^2 = 11,970,588,672
For 2 eyes, 1 egg - 6 * 14^2 * 3 * 2 * 2256 = 15,918,336
For 2 eyes, 2 eggs - 6 * 14^2 * 3 = 3528
For 3 eyes, 0 eggs - 4 * 14^3 * 2 * 2256 = 49,523,712
For 3 eyes, 1 egg - 4 * 14^3 * 3 = 32928
Total - 1,300,585,570,172

2. Non-strict Eighth rule version - Tar Mother eyes and eggs can all coexist at any different states.

For 1 eye, 0-3 eggs - 4 * 28 * 2259^3 = 1,291,120,317,648
For 2 eyes, 0-2 eggs - 6 * 28^2 * 2259^2 = 24,004,893,024
For 3 eyes, 0-1 eggs - 4 * 28^3 * 2259 = 198,358,272
Total - 1,315,323,568,292

Case 6. - The 2*2 pillar is the floor square:

Total = 17

Case 7. - Serpents and all single square objects and monsters, except Tar Mothers:

1. Strict DROD rule version - Eggs must be all of the same age.

For 1 length 2 serpent, 0 eggs - 8 * 4^2 * 2256^2 = 651,460,608
For 1 length 2 serpent, 1 egg - 8 * 4^2 * 2 * 3 * 2256 = 1,732,608
For 1 length 2 serpent, 2 eggs - 8 * 4^2 * 3 = 384
For 1 length 3 serpent, 0-1 eggs - 8 * 4^2 * 2259 = 1,156,608
For 1 length 4 serpent - 8 * 4^4 = 2048
For 2 length 2 serpents - 8 * 4^4 = 2048
Total - 654,354,304

2. Non-strict Eighth rule version - Eggs can exist at different ages.

For 1 length 2 serpent, 0-2 eggs - 8 * 4^2 * 2259^2 = 653,194,368
For 1 length 3 serpent, 0-1 eggs - 8 * 4^2 * 2259 = 1,156,608
For 1 length 4 serpent - 8 * 4^4 = 2048
For 2 length 2 serpents - 8 * 4^4 = 2048
Total - 654,355,072

Case 8. - Serpents and all single square objects and monsters, with at least 1 Tar Mother eye:

1. Strict DROD rule version - Tar Mother Eyes and eggs must all be in the same state, and eggs cannot exist if the Tar Mother eyes are closed.

For 1 length 2 serpent, 1 eye, 0 eggs - 8 * 4^2 * 14 * 2 * 2256 = 8,085,504
For 1 length 2 serpent, 1 eye, 1 egg - 8 * 4^2 * 14 * 3 = 5376
For 1 length 2 serpent, 2 eyes - 8 * 4^2 * 14^2 * 2 = 50176
For 1 length 3 serpent, 1 eye - 8 * 4^3 * 14 * 2 = 14336
Total - 8,155,392

2. Non-strict Eighth rule version - Tar Mother eyes and eggs can all coexist at any different states.

For 1 length 2 serpent, 1 eye, 0-1 eggs - 8 * 4^2 * 28 * 2259 = 8,096,256
For 1 length 2 serpent, 2 eyes - 8 * 4^2 * 28^2 = 100352
For 1 length 3 serpent, 1 eye - 8 * 4^3 * 28 = 14336
Total - 8,210,944

[Edited by agaricus5 at Local Time:11-14-2004 at 10:57 PM]

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Zaratustra00
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Do scrolls with different texts on them count?